Why another "tips" guide?
I saw quite a few guides here with a similar conceit to this one but not many for v2. Since Paradox have sadly put Imperator on the backburner, I figure now is the perfect time to put out guide since it won't be obselete in a week. Having said that, there are a lot of good guides even if they may be a bit old. The wiki is also an indispensible reource, particularly with regards to mechanics so I won't be delving into that so much unless I feel a mechanic is not really explained anywhere.

This guide's focus
I enjoy playing wide with a tech focus, on normal ironman difficulty aiming for achievements. That means if you like to play tall (which is great, diversity can only be a good thing) you may not want to apply everything here. Also I wouldn't call myself an expert (some systems I still only have a tenuous grasp of), nor have I crunched numbers to figure out the best investments or anything. Which means this will probably be aimed at intermediate players. Hopefully anyone will be able to get something but just so you know where I'm coming from.
Anyway, that's enough blabber, onto the main event...

• Buildings largely don't seem to recoup their costs. What I've been doing is focusing on my capital and a few other potential metropoli (preferably ones with an innate bonus eg. Athens) and turning them into research centres (foundry, academies, libraries). Otherwise, make sure the provincial capital is a city and give it 1 fort, temple and theatre if the culture/ religion needs changing. If there's no city, just build a fort in the capital.
  
• Settlements I do even less with- my rationale is that farms/mines don't actually increase your income unless you fill it with slaves, prevent promotion and make sure the good is actually exported. That's way too much micromanagement for minimal gain for me. Estates at least give you a straight up tax bonus but it still seems pathetically small. The exception is your capital province- the more double trade goods you create there, the more you can use your trade routes for other things.
  
• Save your money for wonders- there are a few game-changers there. Just be aware of the historical wonder's effects, don't go building naval traditions if you plan on conquering Rhodes.
  
• Don't forget to set your region's policy, all being well, to wealth acquisition.
  
• Particularly early, make sure you don't go over the fort limit which in practice is 1 fort up to lvl 3 per province and delete extra forts after conquest. You can increase the limit with investments and military traditions, but I've found 1 lvl 1 fort on the capital (so some joker with 2k men doesn't get free slaves) is enough to hold up forces while being easy enough to quickly assault back if needed.

• Aim for -.2 corruption (increased wages, tech, wonder) and give free hands to your government and governors. Seriously, this was a massive game-changer for me. You get great PI generation and loyal governors, which means loyal provinces. Unfortunately I can't find the guide I got this from, once I find it I'll update this to give give credit.
  
• Yes, deifying your rulers is worth it- the game doesn't tell you but there's a few benefits. Every ruler you deify add 15% to conversion rate and using their omen will give a flat bonus effect. I think the best by far is culture's 25% progress in a tech, meaning you'll always be way ahead. So you should get that one ASAP, the others could wait until you've researched the discounts. Also you get to plonk down a holy site for each (ie. your capital).
  
• I love taking a backward province, building a city in it and watching it grow. Unfortunately, the cost benefit just in't there. So go ahead if you want, but if you're purely wanting best results from your PI, don't.
  
• Always be fabricating. Two types- mass claims against large powers and one off claims against a member of a federation. Yes the latter will give quite a bit of AE, but should be balanced by the cheaper large wars.
  
• Just general advice- it may seem at the beginning of the game that PI is very expendable on cities/ investments. This will suddenly show its falsity after early game. If it hits 400, sure go spend it but otherwise hoard it for when you need it for claims, wonders and deifications.

• Researchers: Most important are the bonus traits; obsessive, polymath, intelligent. Especially for the path receiving your deified ruler bonus (see above), the actual growth from the relevant stat may be negligible so it's more important to get the bonus innovations. Loyalty is not important here.
  
• Government: Youth is more important than the base stat. There's no point putting a 60 year old guy in with 15 martial since his statesmanship will mean he never gets above 5 effectively. Loyalty is also vital for PI. Some positions may not be important to you too (eg merc maintainance) while others will be more (eg AE decay). You could use the tutor role (civ level) to train the next diplomat (AE).
  
• Governors: Finesse, preferably great family. You may draw a line somewhere (mine's 4 finesse), after which you use minor characters. Pay attention to loyalty and corruption as these will affect their province's loyalty. I haven't seen evidence of zeal influencing anything despite what I've read elsewhere but please correct me if warranted.
  
• Generals:Best martial after more important positions are filled. Minor characters are fine, loyalty is very important.
  
• Admirals: Great family, low finesse. Basically somewhere to dump your unwanted guys to keep them from being scorned. You can always swap in an actual admiral if you're about to fight a naval war but it's usually unnecessary.
  
• Have a look at the tooltip for your ruler's stats- I'd say in order of preference it would be zeal, finesse, martial, diplomacy
  
• While you're small and therefore have a small character pool, it may be worth poaching characters, especially if you have no good candidates for research. You can get some real Football Manager vibes going trawling through the character search, just remember you'll want them no older than 30 to make the whole befriending then recruiting worthwhile.

• Have at least two fleets- one purely of liburnians (the fastest) for transport and the rest for a siege fleet.
  
• Don't entirely neglect your fleet, but I wouldn't pour tech or traditions into it.
  
• I used to rush for "Cohorts" tech to raise legions from all of my provinces. However, while it never tanked my economy, it definitely kept it from ever taking off. Just having 4 10ks seemed far cheaper while still being able to wage war fine, simply requiring slightly more prep (marching Egypt's levies into place each time).
  
• My legions, for what it's worth consist of: 1 engineer, 8 Heavy Infantry, 6 Horse Archers, 2 supplies, 4 elephants. Yes I know that's 10.5k which is a bit annoying but I found 1 supply wasn't enough for a campaign. 2 width on the flanks, otherwise HI seemed to pop out there. Definitely open to advice here, but these can beat 20k levy stacks, usually even 30k.
  
• When fighting a major power, I'd raise a large levy to go with each of my legions. I might raise 1 or 2 extras if I thought it was needed. The legions provide fort destruction, speed and are the spearhead, the levies provide the bulk to fight those 50k stacks.
  
• Levies seem to be great for military experience surprisingly. Drill your legions whenever you can too and shoot for experience decay reductions.
  
• Have a leaderless 1 engineer/9 Light Infantry stack to build roads. These don't need to be too intricate, just make sure you can move your army to your borders easily, even without boats.
  
• Mobility, as in most wargames, is key. Getting the speed innovations and particularly force march is very useful. You can't set and forget it like in EU4 (be aware of the debuffs from using it) but it will let you choose your battles and make for shorter wars.

• I can see the bones of a great system here but sadly its implementation is, tbh, terrible.
  I aim to get at least Blood of Argeads (Epirus) and continue whatever bloodline I started with. Arranging a marriage with another great family seems expensive and it can be tricky to find someone from your own family.
  
• My (admittedly creepy) solution is to make sure I always have a few small, monarchical vassals (feudatories are best). Then every few years, star one of their girls (12-15) and arrange a marriage with them for your family. If it works you'll get an event when she turns 16, unfortunately it often doesn't and she'll marry some other loser. That's why you keep her starred, if you're lucky you'll see when she turns 16 (the offer will 100% work then) or try somewhere else.
  
• If you have good relations with other nations it's a lot easier, I just always have AE tanking relations.

Please comment with remarks or questions, I'll answer as best I can. Thanks for reading!