Probably a little bit of everything, but less on the crowds. We want to ski some of that famous Utah powder! Hopefully I can make it the whole week!
Would you suggest just staying in downtown SLC or is it more fun to stay up on the hill? I think the idea right now is to hit 4-5 resorts. I'm not really familiar with the area and I don't know how far away everything is from one another.
So if you're wanting to hit that many places, I'd find a place in Salt Lake City / Midvale / Sandy. This gives you a nice central location and then you can go to different resorts more easily. If you were to base in Park City or Big or Little Cottonwood canyon, you'd end up driving twice as far when you want to go to another place.
Basically you have Alta and Snowbird in Little Cottonwood Canyon (LCC). Alta is skiing only and Snowbird doesn't have much beginner/intermediate terrain. Good snow, but they get crowded.
Big Cottonwood has Brighton and Solitude. Brighton has a lot of snowboarders and Solitude has a good mix of terrain and very few people skiing it. That's probably your best bet for uncrowded and good snow.
Park City has PCMR, the Canyons, and Deer Valley (also skiing only). PCMR is more known for terrain parks. The canyons and Deer Valley have better terrain. If you stay up there, there's more apres-ski, shopping, nightlife, etc. It's more like a traditional ski town, where SLC is just a normal city and Sandy/Midvale are typical suburbia.
You should also hit Snowbasin and Powder Mountain, which are towards Ogden, but a reasonable drive from SLC. Those are also likely to be less crowded. Snowbasin has everything from challenging technical terrain to the best high speed rolling groomers around, great lifts, and spectacular lodges. Also a super nice restaurant at the top of the mountain that's worth eating at. Powder mountain is very uncrowded and quaint. You can get untracked powder by skiing off the side through the trees and catch the bus at the bottom, and they also have extremely cheap cat skiing there as well.
I'd go with one in each area for the overall experience.