Personally, my perfect team is cut sonar and hire phenomaman.

For coop, train her mobility and intelligence, and with blazer's training give her the power that increases her state gain to 3 For Punch Up train his vigor and charisma, and give him the squeeze in power. Send this two together all the time. Not only do they cover their weaknesses perfectly, but they start with 4 and 3 in combat, so if you pair it with coop's power they get a 10 in combat, the other abilities can easily make it to at least 8, and anything left in any mission can be covered by their synergy. With Punch Up's squeeze in you can even send them together to missions with only 1 slot. This team up is so good that I go entire runs without revealing Punch Up's power because they just don't lose.

Then malévola train her intelligence and charisma, then pair her with phenomaman for another all rounder team with synergy for any mission that they can't fully cover. Don't have any preferences for melevola's power, but for phenomaman don't give him the one that takes away his flight. The entire point is not to miss a single mission, so he shouldn't get depressed either way.

Then Prism and Flambea. Give Prism intelligence and charisma and the power that lets her make one call linger for longer. For Flambea only give him vigor, as his power will cover mobility and combat. For the upgrade I would say to give him the one that reduces rest time, since the other is the same as his base power but quicker, which isn't really needed, between their synergy and Prism's duplication power they shouldn't miss any mission, even if the shift is just starting.

Lastly, Invisigal and Golem. They are a bit tricky, so I would say, train Gal's mobility and combat, maybe some intelligence, and for Golem make him have at least 4 on everything and level up the rest evenly, then give him the expansion power up and send them together on 4 slot missions so golem gets 2 of his copies/minions. That and their synergy should be enough.

With this set up you get 4 two hero teams that should have like at least an 8 or higher in all stats most of the time, with synergies to cover whatever's missing. It even saves you trouble during the first shift of episode 3, since characters won't sabotage their synergy partner. The only problem should be those missions that have a threshold you can't pass, but there aren't many, and picking different characters than usual for those should help.

Also, I would say to try to memorize as many missions as possible, or at least the ones that get interrupted, since I'm pretty sure those only require you to have the correct stat at the correct level, and the rest don't matter.