You do realize that the tow vehicle requirements and the trailer situation are going to be linked together. Thinking about the truck is something you should be doing just as you are looking at trailers.
A critical item to consider for the tow vehicle is not the length of the trailer but the weight. Do not get caught in the empty vs loaded or max weight issue. The weight you need to consider is the max or GVW (gross vehicle weight) of the trailer as no one tows an empty trailer to use, especially full time. Keep the weight capacity of the truck in mind when looking at the trailer.
A very general towing capacity rule of thumb is this.
Half ton truck, about 7000 lbs max.
3/4 ton truck about 10 to 13,000 lbs max.
1 ton truck about 12,000 to 17,000 lbs max.
Yup there will be trucks in each of those categories that have less or more towing capacity based on all of the ways they are equipped but those are ball park figures to consider. If you are at a RV dealer and the salesman says you can pull anything with a 3/4 ton, leave. He's lying just to get your money.
Fulltimers generally go for the longer trailers for a couple reasons. You need room to stretch around inside when stuck indoors due to weather conditions and you will be carrying your "stuff" (tools clothes hobby stuff and so on) since that is now your HOME.
That means a decent sized basement for storage and a reasonable cargo carrying capacity for all your stuff. That is weight of materials you will be loading into the rig to use while living in it. That also includes a minor item like fresh water tank capacity as well as black and grey tank capacity.
Do NOT overload the trailer (and or truck) as it will end up causing you tire failures, suspension problems and lots of expensive repairs. Keep in mind that once you get the load going you will have to be able to stop it as well.
A fifth wheel trailer will provide the most room, cargo capacity and towing ease than a bumper pull or travel trailer will. That will require a long bed truck and 5th wheel hitch. There's that pesky truck requirement stuff again.
Look at the various dealers in your area. Get names of brands of trailers and look them up on line. You will be able to access floor plans and pics of the units on the manufacturers or dealers web sites. Look at as many brands and models of units as you physically can. Being there in person will tell you more about how the unit "feels" inside than any number of pictures. Slides are heavy but without them you have far less resell options and far less room inside the rig.
Figure on buying a used unit. Learn what to look for (water damage, body damage, appliances working or not, general condition) to see if a rig is worth considering. Make sure they demonstrate every appliance and feature on the unit works BEFORE you buy.
Remember that many brands, including top level full timer names like Teton and Travel Supreme are no longer in business. That can make support later on problematic with or without warranty concerns.
Go to this website http://www.rvnetwork.com/index.php?
and join the forum. it's free. There is more info about full timing there than just about anywhere else.
Ask questions when you see something and do not be in a hurry to buy.
You mentioned desert heat. Take it from one who is an AZ. native and has spent more than one summer there in the heat in RV's. If the trailer is over 25 feet long, you will almost certainly need 2 air conditioning units on it. Anything over 30' it's guaranteed you will need dual 15,000 BTU units to stay comfortable. That also means you will need shore power or be prepared to spend very big $ on generator fuel for a BIG generator system to run them. You will spend less in a park than dry camping like that.