Ok you didn't ask but I can't resist lol.
So, rugby isn't like american sports where it's all centralised in one top league. Instead, there are a few different ones in different countries. On top of that club rugby isn't the highest level of rugby, the highest is Internationals.
Rugby is played all across the world, but due to time-zones, proximity etc. it is basically treated in terms of two halves - the Northern Hemisphere and the Southern Hemisphere. The south was historically the best (sort of), but that's not true any more.
In the Northern Hemisphere there are three different leagues - the English (Gallagher for sponsorship reasons) Premiership, the Guinness Pro14 and the French Top14. Neither is clearly better than the other, just depends where you're from which you watch. The premiership and top14 are only English and French teams respectively, and the Pro14 is the clubs from Ireland, Wales, Scotland (used to be called the Celtic League), Italy and since last year - very strangely - two South African teams (used to be Pro12). I would say that, though I am obviously biased, that the Pro14 has some of the most entertaining play. The French league has the most money thanks to a huge TV deal and a massive salary cap, so they import a lot of great players from the southern hemisphere. But the style of play isn't always that great. There is also a European Cup which the best teams from each league qualify for.
In the Southern Hemisphere there is one league called Super Rugby - teams from New Zealand (the best by a massive margin), South Africa (historically a rugby crazy country with good teams, but less recent success), Australia (they prefer rugby league there, the clubs aren't that great), and one from Argentina and one from Japan. Super Rugby would be one of the best competitions to watch, very exciting and open style of play.
Each hemisphere has it's own international competition too. In the North it's the Six Nations - England, Ireland, Scotland, Wales, France and Italy, in the South it's the Rugby Championship - New Zealand, Australia, South Africa and Argentina. But there are also yearly Test windows in the summer and autumn when teams from the north plays teams from the south, these have just ended for this year. Then every 4 years there is the Rugby World Cup.
To watch in the US seems like it's divided up across a few different ones (maybe you have some already, not sure how it works).
https://www.nbcsports.com/gold/rugby seems to have the English Premiership (obviously good quality too, and I am biased, but meh...), the European Cup and the Six Nations.
https://plus.espn.com/denied?block=geo ESPN+ app seems to have all the Pro14 games, maybe some like the final will be on ESPN3 or something. I believe you also get Super Rugby too.
There is also some thing called florugby, but no idea what they have really.
If you start watching you'll pick up the players I am sure.
