OK, since I've been a DJ since 1980 on college radio, I can speak to this. There are two ways to go:
FCC approved
Pirate
If you want to go FCC approved, you need a license to broadcast. Of course, you need the wherewithall to broadcast too. Buying an approved station is one way. That's expensive. It can be millions.
Starting a station is another possibility. You need FCC approval. In areas that are fairly saturated, that can be difficult and very complex. You likely need engineers to design the system including antenna radiation patterns to insure you don't step on other stations' frequencies.
You might want to do what I did, because your motivations look pretty much like mine. Find a station where you can DJ. My station (KALX, Berkeley, 90.7 FM and streaming) is a university owned radio station. However, the core of the personnel are community members. A good percentage at any one time are university students, and their turnover is higher than for community members because a student's life is more in flux. However, if you are into it and dedicated, you can remain on the staff. We do yearly fund raisers.
We have a huge library of around 115,000 items (LPs, CDs, 12", 10", 7" records each count as one item). As a DJ you can play anything that isn't prohibited by FCC rules including things in our library or material you bring in personally. Those rules used to be scant when I started, but nowadays are more stringent. Mostly it's about not playing songs with around 7 forbidden words. However, sometimes it's objectionable content (not often). A station can be fined, sometimes a whole lot, or worse could happen from the FCC.
The FCC has rules that have to be followed including EAS tests (emergency alert systems), logging, etc.
If you are a pirate, you don't have those rules but you might have to watch out for the authorities, possibly.
We log for around 1 week out of the year the writer of each song we play. The rest of the time we log artist/title/label for each song.
If you broadcast by satellite you don't have the same rules, you can play stuff that we are not supposed to play including the "bad" words.
For several years now, we have been streaming in several formats from our website. I think most college radio stations stream now as well, at least the bigger/better ones. You could start an internet-only station.