Steve,
I have towed a trailer that size with a Tahoe. Also with an F150 with 3.42. My advice would be to not buy anything close to the tow rating. Smaller is better than larger when you are towing with a 1/2 SUV with a 3.42 axle. The wind resistance is a big problem with a TT; you would see a big difference towing a 5000 lb flatbed trailer versus a 5000 lb TT.
We started with that TT. Then a couple of fifth wheels and 3/4 diesel truck. Then a 23' B+/C, and now a 25' C. Class Cs are a good compromise. You get the benefits of a MH, with reasonable affordability of purchase, maintenance, and gas mileage. The biggest downside to me is that build quality typically is entry level. The same can be said of TTs, though. You have to get educated about how to check the cabover for water damage. Then if you buy one without water damage, learn how to check and maintain the roof and seam caulking.
For the kind of traveling you are talking about, a TT would get old in a hurry, to me. I feel TT's are optimum for a "trip to the lake", where you tow for half a day, park the TT for a week or two, then go home. The daily grind of towing a TT across the country would get to me. Fivers are a different matter. They are much easier to hitch, unhitch, and set up, and they usually tow like a dream.
Bottom line, for your kind of trip, some sort of MH would be the best choice IMO. Either that or a pop-up tent trailer or compact TT. Any Class C you buy should be able to tow a small car, although it would be worth verifying it.
On a budget, I would buy a high mileage ex-rental. When the question comes up here, people who have never owned a rental post that it is a terrible idea. People who own them post how happy they are with their purchase. What you get is a well-maintained rig that is not very old, but with mileage. Here is a thread on them:
http://www.rv.net/forum/index.cfm/fuseaction/thread/tid/26035008.cfm
