There are a couple of ways:
Self Sponsored - You pay for everything, including clothing, gun, ammo, gear, etc. If you go through the full time class, it will take about 3-4 months to complete. And the fgull time class is held at POST in Salt Lake County.
If you go through one of the satellite Academies (I think there is one in St. George) it will take just under a year to complete; The first block is 3 months, the second block is about 6-7 months.
In all , I think you're looking at a 6-7k cost total.
The second way - Get hired by a department and have them send you through POST. Then they will cover expenses. Not many departments will do this anymore. Most look for candidates that are already POST certified. However, there are some that still do it.
My suggestion is decide what area of Utah you would prefer to work/ Live in, then research the departments in that area. In the mean time, do a ride-a-long in St. George and ask them about becoming an LEO.
As far as books, there's not much need to study for on going through POST. There are, however, several books about police testing. Go to the local library. They should have plenty of good ones you can check out.