You start game by selecting a pet and 'trainer specialization'.

Pet itself doesn't matter much. You can easily get those pets. They are better than 'common' rarity and roughly equal to 'uncommon'.
Otto is best overall pet if you care about min maxing super early game. It's most efficient for mining and training out of starters.

Specialization matters - pick mining.
It's the most important mechanic in the game for a really long while.
What specialization does is give you a certain amount of investment into 'player level' skills.
While you eventually max them all out - that's only in super late game so order of unlocks matters a lot in how fast you progress.

Once you start the game - start by putting your pet into mining ores.
Augment your pet to clone it and keep mining to unlock all mechanics really fast.
I will summarize all mechanics in next sections.

Mining - mining depends on attack(damage to ores) and stamina(how long you last before requiring a rest) stats.
Otto out of starter pets is best option.
Best pre legendary 'rare' pet is 'Shellbunny'(pet #7) - it has maximum leveling speed(hidden stat) and best attack/stamina combo.
Best mining pet 'spirits' are Snake and Bear for attack. Turtle/Ostrich are for stamina.

Augmenting pet with ore you plan to mine gives double damage. Pretty much mandatory. Do try to first make base pet a 'perfect' one at least in terms of attack/stamina.

At first you will want to augment loads of 'amethyst'(purple) pets. Those are most efficient for quite a long while. In fact it's super efficient for it's HP amount.
At very high levels with good attack values and attack spirit they will be able to one shot some stronger ores even without double damage. But by then you will be getting either bunny or legendary pet.

1st legendary pet and Shellbunny should roughly be able to 1 shot Emberite ore with double damage and attack spirit.with staff lvl ~10 and maxed damage from legacy while being closer to level 100.
When they have 75% attack. Meaning augmenting a 100% attack pet.

Stormheart one shotting is quite far. For 1st legendary pet that would be ~level 19 staff and lvl 100 pet.

For Stormheart and Harmonium ores you generally want final legendary pet basically.

Remember that main use of mining is getting cash. And main use of cash is investing into legendary pet currency ASAP.
Game has very few pets and you only really need 1 copy of each to perfect it. This can be done at any point in the game really fast via 'trade' mechanic, hence rushing best pets is min max way.

Training
In this tab your pets are fighting enemies. Main use of this is getting 'soulstones'. Those are a way to get pet
Most important location to farm here is 2nd one. It has 'Shellbunny' - best overall pet for pretty much everything. Pre legendaries obviously.
You will need 6k fragments but it's worth the wait.
Pet you put into training is not too important. What matters most is your attack value. And you should have enough for 2nd area.

It's entirely possible you will get some doable trade for Shellbunny earlier, but that's RNG.
This is a 100% safe method but it requires running game in the background for ~30 hours(divided by amount of 'multi tasker' slots).
It's also possible you will get legendary pet faster if you can rarely afford to keep game running.

Once you get Shellbunny - just farm area you can one shot with max attack shellbunny that has any attack spirit for maximum account experience.
All stats have some effect in the training tab but attack is by far most important.

Exploring
Exploring tab has 2 actions you can do - explore and gather resources.

Exploring is purely for unlocking new locations. Once you unlock all areas - pet slots for it entirely disappear.

Gather resources is some income + getting currency for 'artifacts' which is very important.

Both are also best source of exp for pets.

Exploring needs only 2 stats: Stamina + Speed. Total value of those seems to affect the speed of exploration/gathering. You need ~750 total 'stam + speed' to instant clear.

Technically speaking - Archowl or Fox(both starter) lvl 100 with max speed/stam genetics and a spirit for speed or stam is enough for instant explorations/gathering.
You might also need lvl ~5-6 staff of exploration.
Shellbunny is easier and also levels faster however.

Best spirits are Deer/Bird for speed and Horse/Ostrich for stamina.

Some say stamina has bigger impact on gathering and speed bigger impact on exploration but it's hard to confirm it.
It's easy to reach the point where you instant complete the progress bar each 'tick' so it's not too important.

Gardening
Gardening is how you unlock legendary pets - best in the game by far.
There are 4 in total. Each better than previous. Price increases each time.
10m>50m>500m>10b

Gardening is where you need to spend most of your cash past unlocking some cheap mining ores.
You need to rush unlock better plants as they are by far more efficient per coin.
Only final 2 really matter.

Each plant is roughly x5 the value of previous.
With final plant lvl 1 you unlock 3rd legendary pet in under a day and final pet in a bit over a week.
So you probably want final plant at least lvl 2.

Once gardening is fully complete - you will be getting coins instead of income at a ratio of 20 garden currency for 1 fable coin.

For example with lvl 3 final plant and everything else lvl 1 - you will get ~8k per 5 sec.
It's mostly there to help you reach 1 billion for achieve a bit faster.

Soulstones
For each kill in 'training' you get a soulstone. Main use is rush unlocking Shellbunny from 2nd area.
Other than that - trading is generally more efficient for getting new pets.
Starters are super cheap, common are relatively cheap too. So if those are missing from trade - it might be worth getting those via soulstones.

Magic
Here you craft artifacts from resources that you grind in exploration tab via gathering. Staff of mining and breeding are most important.
Both save you cash.
Exploration is useful to have on level ~5 for much easier 1 tick completions even with weaker pets. After which it's kinda useless.

All staffs are 5% to their bonus per level.

Once you unlock all 4 staffs - you also unlock final 'magic' staff.
It allows you to craft potions. I found most of their uses inefficient since artifact resources are one of biggest limitations in the game. Maybe spirit swap can be considered for harmonium pets.
It also allows you to cast 3 spells - trade extension, refresh trader and summon new creature.
I would say those are too expensive to be worth.

Legacy Upgrades
Each skill has some starting cost and cost increases by 1 for each purchase.
You need to max them all for an achievement but that will be one of final achieves you complete.

Mining:
Most important early on - it allows you to get more cash for rushing legendary pets and hence min maxing your mining efficiency of harder ores.
Pretty much everything aside of autosell is really important.

Training
Multi tasker is the only important thing here if you plan to rush unlock bunny pet.
If you don't plan to - entirely skippable until end game.

Exploring:
Get 1 explore and 1 gatherer slot ASAP. But do NOT go over 1 explorer.
You only have 11 locations to unlock so it's pointless to have more. Once you unlock all areas - exploration entirely disappears so you can't even gain exp with it.
Gathering slots still remain super important so you will want all 3 before long.
Artifact resource is roughly on par with mining/gathering slots in terms of importance.
More exp is also quite neat.

Magic:
Pointless automation.

Storage:
Consider adding 1 point here and stop for a long while after that. For practical reasons that's more than enough.

Augment
Augment is how you 'clone' pet. Mainly used for trading or mining and initial breeding.
Can only be done from non augmented pet.

Trading
Trading is easiest way to get non legendary pets.
Every hour you spend with game running gives you a way to get 6 random pets.
Usually roughly 1 starter, 1 common, 2 uncommon, 2 rare.
Sadly they aren't always 'base' versions.

Breeding
Breeding is main way to improve pets genetics and vibrancy.

You can only breed same pet(but also the augmented versions of it)
When you breed 2 pets - you get a random 'augment' type between parents. Remember that only non augmented version can later be transformed into augmented one of your choice.
I recommend switching up breed order of pets if RNG seems to favor giving non normal augment.

You do NOT lose pets you use.

Breeding is explained more in depth in my 'how to get perfect pet' section.

Combiner
Here you can combine 5 ANY pets.
You get a random one with genetics randomly selected from all pets and a random vibrancy value.

Honestly I didn't find much use for this. Breeding is just more efficient.

Gene Modification
Allows you to use late area resources for improving genetics and changing 'spirit'.
Can be useful for high rarity pet min maxing.

Your Creatures
In this tab you can check base stats of pets and release them.

Collection Log
Shows progress towards game completion.
Hardest achieve in the game needs not only getting all 492 pets(41 + all augments) but also all of them being 100% vibrancy.

Breeding the perfect pet
You mainly get perfect pet via breeding.

I assume you start with 1 'base' version of pet. Likely one you got from trading. But soulstones are guarantee if you can't luck out in trading.

Now step by step:
1) Augment it with cheapest ore you have.

2) Breed it while inserting 'base' version as one of the slots.
This will give you 2nd 'base' version pet before long(it's random which you get)

3) Now that you have 2 base version pets - keep breeding them.
Eventually you will get max/100 vibrancy(10% chance)
From now on ensure at least 1 pet has 100 vibrancy. This bumps chance of keeping 100% vibrancy to 60%.

4) From now on you are simply combining higher genetics pets while ensuring at least one has 100% vibrancy.

Remember to utilize the 'breeding staff' to lock a '~100 stat' you randomly got onto another pet.
This ensures you will keep getting 100 on this stat via both average and highest parent while waiting to roll some other stat as close to 100 value.

Should barely take any time to reach 90%+ genetics.
It's important to note that you are ALWAYS progressing by 1 stat if you average or high roll some stat that is equal on both pets.
So reaching 100% genetics is easier than it sounds.

To reduce price of breeding you will want breeding staff level as high as possible.

A perfect pet will get augmented into a 75% genetics pet.so for perfecting augmented versions you will also want to repeat process by breeding the augmented versions instead.

Which pets to focus on?
Start with Otto starter pet for all your mining needs and 'training'.
Fox or Owl for exploration/gathering. A perfect speed/stam one with speed or stam trait should be able to complete explore/gathering in 1 tick.

Later:
I would say for simplicity - simply do Shellbunny rare pets for all content until you unlock legendaries.
Those bunnies are simply too good overall paired with maximum exp gain speed.

Legendaries have slowest exp gain.
There are 4 of them and each is better than the other.
You get them from garden one by one from weakest to strongest with increasingly high price.

First legendary has stats of 100/110/100/120/120 - slightly better than bunny overall but much slower leveling.
Final legendary has base stats of 130/180/140/200/200 HP/ATK/DEF/SPD/STAM

There are 3 achieves that can possibly become your limiter:
1) Max out all legacy upgrades. Most likely candidate. You can only level up when game is running. So unless you have game running in background full time - you will almost certainly be stopped by this achieve.
You will need player level ~240.

Ensure that:
Exploration is being 'one tick completed'.
Training on level 90-100 is 'one hit killed'.
Level as many harmonium barblades to 100 as possible and use them to mine harmonium ores for maximum exp via mining.
With all mining related legacy upgrades - level 100 barblade(final legendary pet) can one hit kill a harmonium ore with 75% attack and level 21 mining staff even without 'attack' spirit. As long as it's not attack debuff spirit of course.

Also get all related exp bonuses maxed from legacy ASAP.

2) Have entire creature collection with 100% 'vibrancy'. You don't need to keep the creatures.
Getting 100% vibrancy on 'normal' pet should be ultra trivial. After that it's just a matter of getting enough currencies to augment it as the vibrancy is kept at 100%.
Only final 2-3 currencies will likely limit you if this becomes your limiter. But that's pretty unlikely.
Currencies are only gained when online but so is player level and player level should take longer.

3) 1 billion fablecoins - just a matter of time. Garden will give pretty good income after you finish getting legendary pets from it. After you do that - this achieve can be purely idled, so even if this remains your last achievement - you will finish it by just forgetting game for a few week or so and then launching it.