Are you able to get wine shipped to you in Utah? If so it might be easier to give you suggestions of that sort. Hard to know what sorts of bottles might be in your local store.
For Rioja anything by López de Heredia or La Rioja Alta is going to be very good and typically a fair price.
For Cotes du Rhone -- there isn't a lot of bad Chateauneuf du Pape (though be weery of anything <$40 -- it's just not possible to make good CdP for less due to land/fruit prices). If you want to spend a little less, look for a bottle that says Gigondas.
There must be some DBAC in town that wine folks buy from and has someone who knows that they are doing. If you can find that place the way I would ask is:
"I'm looking for a Gigondas in the $30-50 range" or "Do you have any classic style Riojas for around $40?"
Honestly -- you're gonna have a lot of hits/misses as you discover your palette. You'll have overwhelming bottles for $20 and underwhelming $50 bottles. You may discover you're a Buster and are a true fan of one varietal or production style and start zeroing in. Or you may discover you're like me and you dig a wide variety of stuff from the perfection of Burgundy to weird ass skin-contact wines from Georgia.