Back in my day we used Mixcloud. Similar to Soundcloud but geared towards shows and sets rather than single tracks. Uploading can be a pain though unless you're on a fast connection. I remember my 2 hour show taking an hour and a half to upload. Imo its best feature is that you can type up or upload a text of the playlist and it displays it as you listen along. Here's an example https://www.mixcloud.com/Cyclopsean/rage-rage-w-king-seanie-g-7-5-12/
We used Rivendell Audio. It works quite well once you get it set up. It's open-source and runs on Linux boxes so you definitely need a sysadmin who knows his linux systems; alternatively, you'll need a ton of patience. There's a bit of a learning curve for the Jocks as well since it's mostly designed for full automation and people will forget to reset the playlist for the correct times if they stop the playlist (called a "log") to play tracks from CDs or vinyl. It does give your PD a lot of powerful tools to schedule and manage music that goes on the air. And it allows for easy voice-tracking so you can maintain a Theater of the Mind in which there are DJs manning the station 24/7.
Personally I think it's worth the effort to implement it if the station as a whole is willing to embrace it. When we added it we ran into a lot of resistance from people who romanticized CDs and vinyl. Eventually came to accept it and use it.
Have you checked out Airtime?
It's free to download and use, unless you want them to do hosting for you.
It has support for multiple DJs and good logging and charting from what I've seen.
Its only real shortcoming as I saw it is that you can't schedule events (say, a PSA at the top of every hour).
Back when I was running tech for a college radio station, we used Rivendell to run an automated stream. It's got a bit of a learning curve, but works well if you want to have an actual stream for people to listen to.
The station I'm at pays licensing fees to SESAC, ASCAP, BMI and SoundExchange. With all four PROs, it seems like we're fine with what we can play off our laptops online.
I couldn't find anything about it being illegal to broadcast music from Spotify. The only issue you could run into is if ads play in between songs which can then be avoided if you pay for Spotify Unlimited/Premium.
There is a portion of the Spotify terms and services that prohibits "making available to the public any part of the Spotify Services or content delivered to you via the Spotify Services."
If anything, if you use Spotify for broadcast you could run the risk of losing your account. It's not as severe as a fine from the RIAA or FCC so take it as you will.