I'd pack a small duffel with three or four days worth of clothes, plus a shoulder bag for EDC items. In addition, pack enough underwear and socks to last you the entire duration of your trip. (Contrary to what the previous poster said, I would try to avoid doing laundry on the trip. You'll be tired enough just from driving without having to also deal with that.)
If you're going to check a bag, don't be shy about checking knives. I check knives when I fly and I've never had a problem.
Of course, if your bag gets lost by the airlines, then that could really mess with your travel plans. But if you're flying non-stop then the chances of that happening are greatly reduced.
Another option is to simply mail that stuff to your friend that cannot be carried on the flight. Assuming you have some lead time on this trip, the postage for a few small knives probably won't kill you.
I always try to carry a firearm when I travel cross country, even if I have to have it locked when I'm actually driving. As far as I know, in almost all states you're allowed to have a loaded firearm in your hotel room because it is an extension of your own home. That said, a Utah out of state CCW permit can make it possible for you to carry the gun loaded in your car for quite a few of the states that you will travel through. In some states you might not need even that in order to keep the firearm loaded in your car. You'll need to research the firearm laws for each state that you will travel through in order to know what is and is not permissible.
All of that said, there's no good way for you to get a firearm to Arizona unless you're going to check luggage.
Enjoy your trip.