It's been a while, so you'll forgive me if I don't remember specific details...
Shack: Everyone's available by wave 2.
Cave: I forget the specifics... Mucisa appear once the generators are turned on, but I think there's also a minimum wave count...
Alien Ship: Everyone appears once the first... couple doors, I think? It's the room with all the spawning doors that allows Queens in, right?
Jungle: ...I dunno... It's a wave count for Orcs, I assume...
F.E.R: Yeah, if you happen to like Puppet, you're fucked. Foxy's decently quick to access, though.