My info is quite old but mostly still valid. I concur that Utah is the best bet for a good first or even last western ski trip. There is fine skiing at all the resorts and the most reliable snow in the lower 48. One important consideration: have you skied much powder? Moderate-to-deep powder is different, forgiving, 1000x easier than ice, and insanely fun. Learning powder is *very* fast even for a hack skier, under a day if you exert yourself (I'm not kidding.) If you can ski powder, there is little difference between a 35-40 degree slope (common at Snowbird) and a 25 degree slope. For deep powder, 35deg is often *easier* than 20deg.
Many great skiers here and at TGR will sing praises of Snowbasin--small crowds, fine food and lodging, excellent lifts and terrain (just as big as Snowbird, lots of steeps, just not as steep), non-intimidating base area. I'd look *hard* at that. Snowbird has the skiing of a lifetime--if you are fairly fit and have a good attitude, you will treasure the day(s) you skied there. Here's a nice sample, the terrain is typical Bird (terrain, not speed/talent). Just look at how open, soft, and fun it is:
As for Alta...very pretty (but so is the Bird), but not-so-great lifts and traverses to get to the best runs; many great rocks and short, great, narrow chutes all over but they're beyond your ability now. When people tell me they skied Alta, I say, "Great, did you ski Snowbird?" "No." "Pity." It is the best mountain there, better in some ways than Jackson (snow quality, open 35deg+ faces). But...lodging is scarce, so you may need to drive or ride a bus up the ~3000' climb of LCC each morning. But that's not far or bad unless it's closed.
Then there is the super ticket to consider, 4 great areas connected, lodging at 3, but examine the rules, there are some options:
So perhaps start and stay at Snowbasin, and get to the Bird at least one day if you're feeling good about your skiing.
Best of luck.