Look at craigs list for yuma, there are always tow bars on sale there roadmaster and blue ox. There are a couple of wrecking yards there that have/had some when I was looking. Also look at phx and tucson. Many times you can find like new towbars for 150-250$ vs the 9-1000$ new. With that said yes you will need the baseplates and adapters if required to hookup one brand to the other.
Depending on what vehicle you buy will depend on what you need for towing. Old jeeps can just be bolted to the bumper as the one above looks to be. Autozone, orielly even harbor freight have these inexpensive units usually less than $100. Just depends again on what you want to tow. For my 94 ranger they want $400 or so just for the baseplate, but I have seen them on CList for lots less. If I was going where you are talking about I would look for a used small pickup, my ranger is just shy of 3800lbs as a supercab v6, manual trans. If we decide to go up to alaska that is the veh I would drag along. Put a bed cover on it and use it to haul extra stuff. hard bed covers can be had for less than $200 on CList most ofg the time and then there is the option for a camper shell!
Except for the jeeps the use of a bumper installed hookup is pretty slim unless you have a shop weld something up and that will be close to buying the baseplate in price. I know I looked.
There are always used brake systems for sale also. usually less than $250 for a $900 unit.