Buffalo or Rochester. Everyone pretty much flies from here. My only problem is paying a shuttle everyday back and forth to the resort.
If you do PCMR, you won't have to pay a shuttle. If you do the cottonwoods (Brighton, Snowbird, Solitude), you can take the public transit which is pretty cheap. Just make sure wherever you stay is nearby to a bus stop, and you're golden.
Park City proper does get some crowds, and on a good pow day or a Saturday you're going to battle some chairlift lines in the morning no matter where you go that's just the way it is. Stay away from the main/base-area lifts at lunch time and you'll be OK.