Before you look at anything
Talk to a lender first. Not because anybody is trying to rush you, but because the number they give you changes which neighbourhoods are even worth driving. Getting that first means you spend your time looking at houses you could actually buy.
The search
A good search is built on your criteria rather than an automated feed. In Cedar City that usually means a short list rather than a long one, and it often means seeing a house the day it lists rather than the following weekend.
The offer
This is where local knowledge earns its keep. Price is one term among many. Timing, contingencies, what you ask for and what you leave alone all matter, and what works in a competitive week does not work in a slow one.
Inspection and the middle stretch
The inspection period is the part people underestimate. It is not a formality and it is not a renegotiation ambush. It is your window to find out what you are buying and decide what you want addressed.
Closing
Appraisal, financing, title work, final walk-through, signing. Most of this is deadline management, and most deals that go badly go badly because somebody lost track of a date.
None of the above is legal or tax advice. For how any of it applies to your situation, talk to your attorney, CPA or lender.