There are 6 day 1 fights, and you will be given a choice of 3 every time. There is only 1 fight you can actually lose (Viper). Kyver Drone can scale enough to kill you, but this scaling can be avoided by running a board without active items (an item is considered active if it has a cooldown). Like all fights in the game, each PvE will give you one drop randomly selected from all their items and skills. You usually should not focus on buying early items just for the day 1 PvE fight, and should instead focus on preparing your board for the day 1 PvP. It's okay to not have a full board going in as long as you have one by the end of the day.

This fight has 2 fang drops, which is a really good generalist weapon. Fang has a 3 second cooldown, which makes it one of the faster items in the game. It's useful if you have weapon scaling or ways to take advantage of it's low cooldown. The skill drop, deadly eye, gives 5% crit to all weapons. It's most valuable with wide weapons, though having a small amount of crit on weapons is always nice. There's also 2 pelts, which give you 1 gold when you sell them.
Vanessa probably benefits the most from this fight, as she generally wants to play a wide weapons board early, which fang/deadly eye fit well into. Mak can also take some advantage of this fight, as his items generally have a higher CD and fang can help with start time. Magic carpet also benefits from deadly eye. The other characters can do cool stuff with fang and can benefit from the crit, but if your day 1 won't be helped much by that its more worth it to take another fight.

This fight is a little interesting because it scales from slows with the trained skill. If you fight him with a board without active items, you are guaranteed to win because in order to slow there must be slow targets. If there are none, the drone will not scale and sandstorm will always win you the fight.
Trained, the skill drop, gives a weapon +5 damage when you slow. This used to be a lot better when it was all weapons, but it can still be quite good early as a form of scaling. Insect wing is also a really good drop as it reduces the CD of any item, and this fight is always worth considering because of that. It's worth noting that even this tiny amount of CDR is super valuable with poison, as it causes the poison to tick once immediately rather than having to wait the full second. It also works with burn, but that matters less since burn ticks twice a second already. Stinger is an okay bronze weapon if you have +damage, but its certainly nothing crazy. Eagle talisman can give 5% crit to any item, which is alright, and Langxian is kind of a meme item, though it can be workable.
You can take this fight with any character because insect wing is just good, but Vanessa and Stelle both have really good slow packages and can take good advantage of trained. Dooley has plasma grenade, which slows all enemy items, which is also quite good with trained. It's worth noting that Pyg only has 2 slow items, marbles and pepperspray, so it's a lot harder to take advantage of trained on him, though you still can. For stinger, it's worth noting that it goes up in slow targets on upgrade, which you can get at curio or level up, but it's still a 7s CD item so it's still nothing crazy.

This fight will kill you if you don't do enough damage or healing. It poisons you for 3, and then fang keeps stacking a poison every 3 seconds. You don't actually need that much to win this fight. You either need to be able to deal 75 damage in like ~18ish seconds or have a little regen or healing. Healing cleanses 5% of heal value, which rounds down to 1 with a lot of early game stuff, but you don't need much to cleanse away the small poison this mob deals. I really don't recommend taking this fight if you are unsure, since losing a day 1 PvE fight is really bad and often puts you down xp. It's not like winning the fight gives you anything crazy, though there can be huge lategame upside to the skill Lash Out on some characters.
This fight has two fang drops like the inglet, but one is enchanted with toxic and scales poison as a function of 5% of damage. You need to scale a lot of damage to get +poison on this, so it's not really that crazy, but poison is decent early game so it can win some matchups. Extract, +1 poison on any item, is nice for poison builds and the gland gives +1 regen which is nothing to write home about. Lash out, the skill that deals 3 poison at start of fight, can be very good. Lategame it can give you an instant freeze with skills, along with setting up skill chains from that freeze. Some items, like power drill and spider mace, gain charge on poison, so this skill can help a lot. Many day 1 boards don't have healing so this can be some nice free damage, but if they have any healing or regen it won't do much. It has a nice synergy with crocodile tears, as if they have less than 3 regen you immediately start scaling it.
I recommend only taking this fight if you are playing Vanessa, Mak, or sometimes Dooley, and usually even then only if you're playing into poison or have a power drill. This fight is up there with Banannibal in terms of lategame upside with the skill, but it's definitely far from something you should always be clicking. It's also worth noting that Stelle and Pyg have no poison synergy outside of enchants (and cannot get poison skills either) so you should never take this fight on them even if you can beat it.

This fight has a skill that is super valuable if you can activate it, healthy jolt. It hastes your items for 2 seconds on overheal, which is really good. It is somewhat hard to proc if you don't have the proper setup for it, so most heroes don't really benefit. Big money tree builds benefit a lot from this, and Pyg has a lot of ways to trigger heals so it's best on him. You can trigger this on Vanessa with seaweed, but it's usually so late in the fight it doesn't matter. This skill becomes a lot better late if you pick up a restorative enchantment, so it can have a very high ceiling. The other drops from this fight are pretty forgettable, med kit gives +5 heal to any heal item, bluenanas gives 20 max health (it is food which is relevant for dog builds), and duct tape, which gives shield when you use the item to the left of it. Duct tape can help early if you pick up a shielding skill, but generally you want +damage.
This is a good Pyg fight for healthy jolt, but duct tape can be an okay drop if you don't want anything else from the other fights.

This is the fight for burn builds. It has 2 bronze cinders, which give +1 burn to any burn item, and the fiery skill, which is +1 burn to all items. There's also lighter, which is a fast burn item that's pretty good at stacking burn if you can buff it. It plays well with Oni Mask and Eternal Torch/Ruby, and is also a fast tool for Molten Ball Blaster.
If you're playing burn, or want to try for it, this fight is great for it. If you aren't, it doesn't drop anything helpful and you should consider another fight.

This fight has 2 scrap drops, which give +3 shield to any shield item. The real drops from this fight are the skill and silk. The skill, haunting flight, causes a small item to start flying when you first use an item, which can be good for Stelle in most cases. It can also help with launcher core or Mak flying shenanigans, but it also has the added benefit of helping your smalls dodge slows and freeze better. I'm not a huge silk fan, but I do think it can be a good item as long as you focus on doing the quests.
I'm not a massive fan of this fight in general, but silk can be decent and haunting flight has some upside, so I definitely don't skip this always. Although Mak has no shielding I've seen some boards on his character use silk decently well, and his total lack of other shielding makes it a lot better.

Thanks for reading until the end of this guide! If you have any thoughts, comments or feedback, please let me know, this guide is not exhaustive and I'm probably missing synergies or info more experienced players would be able to provide. There are probably other guides on reddit or such that may be better on this subject, but I saw there wasn't much info on steam itself so I figured I would write this.