Watching I would recommend you watch:
* European Champions Cup (mid November- mid May) - which contains the best clubs from England, Scotland, Ireland, Wales, Italy and France.
* Super Rugby (late february - early August) - Which contains 18 franchises from New Zealand, Australia, South Africa, 1 from Argentina and 1 from Japan.
* The Rugby Championship - A national teams competition (August - October) between New Zealand, Australia, South Africa and Argentina. Each team plays each other twice (home and away)
* The Six Nations Championship - A national teams competition (February - March) between England, Wales, Ireland, Scotland, Italy and France. (each play each other once)
* The Pacific Nations Cup - A national teams competition (July - August) between USA, Canada, Japan, Tonga, Samoa and Fiji. A complex hard to explain competition.
* I'm not sure what club scene is available in the USA sorry. I bet there is something to watch. I just haven't searched it yet.
Personally I only watch some of the Super Rugby (All my local team games) the ITM Cup (New Zealand Club competition - My local team) and the Rugby Championship (All Blacks games) + All Blacks games in June and November both involving matches against European nations. Over December and January I don't watch any rugby (gotta have a break. . . . .and I don't have 'the rugby channel' which is the only channel in New Zealand that shows the European Champions Cup > so in other words I have never watched the European Champions Cup before apart from highlights. It was the same for the Six Nations Championship until 2015.)