MOST IMPORTANT CO-OPS TO WORK ON EARLY
These are the co-ops that it would be best to get to a certain point ASAP to enjoy their benefits.
Sadayo Kawakam - Temperance
Main Benefit: More activity time
Kawakami should be an extremely high priority co-op once you unlock not, not because she's a top tier waifu (though she is), but because her abilities are so fucking useful. Basically everything she unlocks is in the interest of giving you more time to do things. First, she'll let you skip her classes to do other things, then she'll work at your house at night to do tasks that normally would have taken time for you, such as making the SP restoring coffee or curry. Then she'll let you skip other teachers classes. Finally, on her last rank, she'll make it so going to a dungeon no longer makes you tired, so if you spend an afternoon doing that, your night is still free. In addition to that, once you max her rank all her services become free. The originally were 5000 yen a pop.
Max this asap. All you'll need is 2 courage, which incidentally is all you'll for another in this teir.
'Chihaya Mifune' - Wheel of Fortune
Main Benefit: Relationship fortune telling
To be honest, half of Mifune's abilities kind of suck. She can tell you what co-op abilities other character have, which is damn near useless because the internet can tell you that. However, at rank 7 she gains the ability to tell relationship fortunes. Like in earlier games, this gets you co-op points with a chosen character, helping to avoid wasting time with "you feel like your relationship will become closer soon" nonsense. The real nice thing is that these fortunes do not take any time to get, though they do cost 5000 yen a pop.
Her co-op requires 100,000 yen and a memento mission to start.
'Tae Takemi' - Death
Main Benefit: Good item
Tae is another good quality waifu cake, but the main reason to go for her link early is to reach her rank 5 benefit, which is the second tier of the stock in her store. Once open she sells and accessory that restores 7 SP per turn. Given SP is basically your gauge for how much dungeoning you can do, this is a really, really nice item. They cost 100,000 yen a piece though. However, Tae's rank 7 perk is a half off discount, so that helps.
Even better, you can get Tae to rank 7 all with just level 2 courage (same as required to start Kawakami's). After rank 7, you'll need 4 charisma, but rank 7 is her last really good perk, so that's all you need to worry about doing early.
VERY GOOD CO-OPS
These co-ops have extremely strong and useful abilities that make it worthwhile to go through them.
Toranosuke Yoshida - The Sun
Main function: Negotiation and Money
This guy is all about teaching you negotiation tactics, the most important of which is the ability to extort demons for large quantities of cash. He makes it so you can keep asking over and over again until the demons get pissed and attack, but this can often be worth it for grinding money. Later abilities make it more likely to get items during negotiations, adding the possibility a demon will become a persona without trying at all and infally the ability to recruit demons of higher level than yourself.
His co-op is a night co-op, which is nice. It requires you to do a part time job a couple of times first, but it's worth it in the end.
Yuki Mishima - The Moon
Main Benefit: XP
Yuki is pretty simple. All his benefits give you more XP. It alternates between general XP boosts and giving your benched party members increasing fractions of XP. His last ability give you universal XP, so benched party members now get 100% experience from all battles. Given that P5 adds swapping characters mid-battle as a mechanic, this is nice as it means every party member can be battle ready at any time and you don't have to babysit so much.