My experience has been that full perimeter-frame trailers are pretty stable to tow, but a lot has to do with how the trailer is loaded and how well the tow vehicle is set up to handle the load. I would caution anyone thinking of towing an enclosed trailer of any size to do so only with a SuperDuty or HD-class truck. I've done it with a half-ton and been blown into the (fortunately empty) next lane by a gust of wind.
Trailers don't tend to lose their value too much as used, but you can save some money that way. In the current economy, a trailer may be a luxury that some need to do without so it may be a good time to buy used.
First trailer i had, paid $1800 in 2005. It was stolen last year and insurance wrote me a check for $2200! I upgraded when I got a new one. Heavy duty axles, dual brakes, full deck, paid $3600 from Anderson Trailers. Added a #10000 winch from Harbor Freight (still works great) for $280 and a tool box also from Harbor Freight, for $125. I love it. I have a 2000 Ford Excursion that I use to tow it.
I just did some towing with my 2008 Exprdition today. Philly to MD. I rented an auto transport from U-Haul for picking up my new cougar. It was one of the best rides of my life. $120 and it is already returned. Gotta love it. I had to \also buy a $30 reciever. All the wiring is there for the brake lighta as I have the tow package on her. Love that truck as well.
Also consider deck height and ramp length. When loading Copy Cats 70 with the front spoiler we have to jack up the front of the trailer and add a lot of lumber to the ramps to get the angle right. We just moved it to his new house in Springfield and now it needs a new spoiler. Its a wooden deck but we treated it and it not slick or anything and the fenders are short enough we don't have the fender problem, we don't like the ramps they are two rails with the cross rail every 6 or 8 inches and the tires fall into the space and make it hard to be precise or control movement.. And by the way we tow it with a Chevy 1500 ext cab Siverado. Brakes are a must but it tows like a dream. Good luck!
Of course if you buy a stock car trailer - you have a handy place to change your oil! ;>) If you can spring for the aluminum, they are very nice, and you can manuever the thing around by hand when empty. they ain't cheap even used. I like the beaver tail ones for ease of loading, especially if you pick up dead cars frequently. Otherwise a full bed trailer gives you more versatility for hauling other stuff too....