The least expensive store in Park City is the Smith's which is located at Kimball Junction at the exit from I-80 to Park City. Smith's is owned by Kroger and it's a decent store.
If you like natural or organic food, then you'll want to shop at Whole Foods which is located in the Redstone Center. This is just past the Smith's on the same side of the road leading from I-80 into Park City.
The biggest, nicest store is the Albertson's. It's located right in the town of Park City at the intersection of Park Avenue and Kearns Blvd.
Have fun here in Utah!
Steve