Can I really only choose from 4 leagues? Is there more available?

Spots in leagues get available at their creation or in between seasons. Today is four leagues, tomorrow might be one or two more (or less).

Yeah; unfortunately you'll have to wait until some leagues go into the off-season--which is when inactive owners get purged--if you want an existing league. If you want a brand new league to get in on the bottom floor, you need to wait until most of the current vacancies have been filled before a new league will spawn, although there are a few right now that are still in the beginning stages, even if you missed the first few opening days of the draft/FA.