For $7k look for a '90's diesel Ford or Dodge (GM 6.5diesel is crap).
Although they are basically bottom of the barrel as far as HP/TQ goes in the diesel world, the 6.5's really aren't all that bad. Prior to '97 they had problems with heads cracking due to poor cooling, and the PMD's tend to die early without an aftermarket cooler, but all of this can be taken care of with several hundred dollars worth of upgrades.
My dad picked up a clean 97K mile '95 1-ton with a 5-speed and with a blown headgasket (and cracked heads) for $3500 off a dealer lot. For less than $2,800 in parts/machining we made it right. Bought it off my dad for $7,000 and have nothing but good things to say about it. I cash crop hay and needed something bigger than my 1/2 ton for yanking wagons with 4 tons of hay on them over the road. Although it may not do it nearly as quick as a duramax/cummins/stroke, it doesn't struggle in the least with any towing I have had to do with it. I get nearly 20 mpg (town and highway averaged).
To the original poster, if you want to do it on the cheap, I don't think a 3/4 ton f250 with the 300 six would be a bad move at all. Again, you certainly won't be overpowered, but as long as you don't live in the mountains or something, the truck should be perfectly capable of pulling a car on a trailer.
If you are looking to spend some more money, and will be driving the truck a lot, it's hard to not want a diesel. Problem is (don't know about other parts of the country) but 200K mile diesels (early 90's or newer) still command a TON of money. And with the price gap between diesel and gas, you aren't saving all that much money with improved mileage.
I don't know where I'm going with all this rambling, so I'm going to just stop now.