I've never seen anyone getting in trouble for running a personal service on your home connection. It's all about the proportion, if you are running a service using up TB of bandwidth/month they'll probably make use of their terms of service but otherwise there's really no reason for them to cut you off.

And what's the difference between running a service like that or just having a public share on your router which a lot of routers come with these days? There really isn't one.

If you want to host it on a service just go with a dedicated server provider and not a "cloud" service which isn't really a cheap way to host a lot of data. You can get a dedicated server with 1TB of hdd, 4GB ram etc. from OVH for 10euro/month. And that's a lot of music.

Edit: Looks like I got ninja'ed there ;)