I much prefer skiing over snowshoes - walking downhill in the snow is for suckers. There are a lot of ways to ski, but the most fun for me is getting off trail and exploring-old FS roads, cutting through meadows, linking up trails. It's a lot like hunting that way, navigating to weird places. Hot laps on groomed trails is a great workout, but I get bored. If you're in western MT PM me and I can point you at a ton of stuff.
What you want: fishscale base, metal edges, BC bindings, no part of the ski wider than 70mm (so they can fit in tracks if you want). You can go anywhere on these.
All you need to know about avalanche terrain is what it is so that you can stay off of it. The Bruce Tremper book is the bible. It's quite easy to be safe if you just never go on avy terrain. This is easier with the setup above, because anything steep enough to slide is very advanced skiing on that gear.
Backcountry touring (randonnee/alpine touring) is a totally different animal. The rule of thumb is you need to be able to ski anything in the resort in any conditions before you take it up. Then you need all the avy gear, training, and mentorship. It's about as involved as hunting to get seriously into.
All that said, snowshoes are cheap and easy and a great way to get out, especially with family. I just find skiing (both kinds) a lot more fun.
Edit: advice for getting started? Rent both and give it a shot. The learning curve is steeper for skis, so don't write them off if the first couple of times sucks. Consider a class, you'll only need to go to one, after that just dink around.