I do SlingTV too, as well as VUDU, Hulu, and Netflix. Streaming via Apple TV in the bedroom, and for the big screen in the Living Room I just did an HDMI cable from my gaming rig and mirrored the main screen since it sits nearby. It's also worth mentioning that NFL Network comes with one of Sling's base packages, and channels like Red Zone, NHL Network, NBA TV, SEC Network, and beINSport are parts of some of the many add-on channel bundles.
If you're looking for more soccer options that aren't included with the channels offered through Sling, there's a decent service for that called FuboTV.
If you're looking for full season packages, your best option is to stream directly from the league like MLB.tv, MLS Live, NFL Sunday Ticket etc.
NFL Sunday Ticket is the only one I can think of that has a restriction of any sort. That one requires a student ID or an address located at an apartment building. I have the latter and it worked like a charm for last season, GameMix and all.