They made it legal to brew. I think its 100 or 200 gallons per year. You'd have to be pretty serious to do more than that. As far as I know wine is ok too. They sell everything for it, but then again they sold the beer stuff before it was "legal" too.
Check out the Beer Nut on 1200 S State. They'll fill you in on all the rules.
Since you are in Logan check out a little shop in Richmond on main street. Very random for a brew store in a tiny town in the heart of mormon country but he has very reasonable prices. Less overhead that the SLC stores so he passes on the savings big time. 25-50% less than the Beer Nut.
Just take your credit card! They'd be more than happy to help you out.
I read that book cover to cover twice before I started brewing. Its a great book, simple with just enough chemistry to help understand how to take brewing to the next level beyond following a recipe.
Check the classifieds for used equipment if you're not in a hurry. I scored two free carboys and another kit complete with brew kettles, two primary fermenters, bottles, cappers, etc for 80 bucks.