an open trailer can be had for $2500 anywhere. an enlosed trailer speced out and nice will run you $6-8000. Clearance issues on the GT aren't bad so you can pretty much get away with any standard trailer.
As far as trailers go any enclosed trailer would work. I myself have a 24ft enclosed trailer that i carry my other cars with... but i recently tried it with my GT. The most innovative idea that I had done, was to put a door on the left side of the trailer directly ligning up with the opening of the door on most cars. It worked really well with the GT. Once inside the trailer, open the door and just step out. Also you might have to install ramps inside the trailer so that the door will clear the wheel well of the trailer. And it looks so cool too..
I have a 24 ft. Featherlite enclosed trailer which I use to haul my cars in. It is all aluminum and therefore saves about 1500 pounds over a comparable steel and wood trailer. I installed a winch in the front that allows me to winch in and out very slowly (I just love that in and out thing :eek ) so I can be extra careful during loading. Heavy duty axels are desireable for long life if you do much traveling. Cost of my rig - $14K. I like it alot.
I picked up my GT in a 20' aluminum Featherliter towed by a Jeep very easily from Virginia to Georgia (400 miles each way, through the mountains). You have to crawl out the window if you don't winch it in.