You've probably already been to the Utah Cycling Association web site http://www.cycleutah.com/
on that site, scroll down on the right to the Utah Criterium series, it gives a pretty good job of directions, sighing up, etc.
For the midweek races there is a crit on Tuesday night and Wednesday night, with an alternating TT or Hill Climb on Thursday nights.
The midweek races are all A (Pro,1,2,3), B (3,4), C (4,5). Start with the Cs and gauge your level form there. I did race against Jeff Lauder in my first TT and its not unknown for pros like Zabriske to jump in the As when they are in town.
You cannot blame lack of available racing in Utah. That is about the one thing I really regret about the move, the abundance of cheap, easy to get to races that are available in SLC and the amazing relatively deserted roads to ride on near Park City. I guess that's two things. Hmmm.