Now that you finished community, you should give DS9 a go! It is the ST series where you don't really need to know the universe to understand it. It's just about a station close to a wormhole linking two quadrants of the galaxy. The rest is up to each episode.
It's fun, because the characters feel "real", unlike many new shows. They're not perfect, and they do the best they can to struggle complex (and sometimes morally ambiguous) situations. Sisko is one of my favorite captains.
Give it a go
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Do you know/like Cowoboy Bebop and Samurai Champloo?