Welcome! I spend some time in Park City myself as my sister lives there and folks have a place there.
As for a good Airstream -- I highly recommend finding one in your price range that is "camping ready" and feels somewhat like what you might do to it yourself. If you put a lot of money into revamping a trailer it can be hard to recoup, so if you can find one that is already up-to-date and ready to camp you might save.
Why not get a fixer-upper? It is easy to underestimate how much work is involved.... especially the first time you do it. As someone new to Airstreams, a better way to get exposure to the systems and familiarity with how things work is in an already functional trailer. After you've had one, it is far more practical to know what you would be getting into should you buy one that needs work.
Focus on the items that can be more difficult to fix/replace such as cabinets, flooring, furnishings, etc. Even draperies. Anything that is "standard" to replace is not as critical -- stovetop, toilet (which many people will replace on purchase anyway) even the fridge, the AC, axles/brakes, wheels/tires, etc can all be swapped out fairly painlessly by just about any RV place or yourself. Rebuilding the cabinetry, furniture, etc is far more specialized, craftsman type work. (This was the mistake that I made.)
Plus, an interior that is in good condition is one sign of a well taken care of trailer.
Good luck and happy hunting!
Texas Gulf Coast Unit, Texas Airstream Harbor
Angelina National Forest, Zavalla, TX