I recommend staying in Park City, either by Historic Main Street (super beautiful, but a little more pricey). I would say a lot of people will be staying in Kimball Junction (about 10 min drive from park city, but more more affordable options. The Holiday Inn and Suites on the travel slide is in Kimball Junction.) Airbnb is also a great option for the area.
Yes or no. Uber works great here. If you want the convenience of a rental car that works too!