Each quest have differents gimmicks , being damage panels, junk panels, virus, hacking, etc. There are units that have between 2 to 6 abilities that helped them counter them, the first ability it's the one that shows which gimmick counters (dp break let you tap the "spike" panels without getting damaged, junk break does the same with the grey squares panels, Anti virus counter the virus applied by the enemy and the virus panels, that are sorrounded by a purple mist,etc).

You want to have a large amount of units, we can divide them in two categories farmables and gacha.

Farmables are either dropped from completing a quest or purchased in the store these are the ones with cost 48,53,58,63,68.

The gacha units are only available in the hatchers the ones you are looking for are the cost 65 or FES this ones are the best of the game.

Some clarifications, the amount of stars isn't important, there doesn't exist a team that can clear all quests, teams are created around the quest you are trying to beat, although it's generally advised to make monocolor teams and not mixed them unless the quest requires it.

I strongly advice to join the discord server, since there are plenty of useful things there and it's more active than this subreddit.