This is a game about auto-battling to farm cute girls. For easy stages, you want to get a solo unit who can farm quickly and cheaply. You'll get to the point where a solo unit can actually generate more resources than she spends. Lindwurm is cheapest, Perrault is easiest to farm, Tiamat, Fenrir, and Charlotte are strongest, and there are a bunch of aoe units that can do it faster in certain cases.
Farming hard stages relies on Invincible Dragon, who you get from finishing the story. She has massive aoe potential and can easily wipe enemy waves herself. An ID team is generally composed of ID, Maria, a tank, and 0-2 other attackers depending on the stage. Again, you want to keep costs down and speed up to make farming easier. Different stages will need different tanks, so there's not really a catch-all. Echidna is probably the best defensive tank and BaekTo is probably the best evasive tank in this kind of team.
Bosses generally require specific teams to beat them assuming you're not strong enough to just brute force everything. Executioner is probably the best example of this; you really want a unit or two with follow up attack for that fight, and you need to position your team to avoid his big aoe.
There isn't really much use for a generalist, all-comers kind of team. It'll cost a lot of resources and will usually take a lot longer to clear stages than an ID team.