I would get a 3/4 ton truck, no doubt about that...
the only question would be the engine and the rear axle.
I think with 6,000 lbs, I would go for a small block V8, like 5.7L. Either 3.73 or 4.11 rear axle. The latter would give you higher towing capacity.
Anything above 7000-8000 lbs or so, I would get a big block gas engine, like 7.4L, or Ford's 7.5L. The mileage is abysmal. Expect 11 or 12 empty, and 8-9 towing. With that, get a 3.55 rear axle.
If towing something heavy and a lot, a diesel, but I have no experience with it. I know I wouldn't want to use a diesel as a daily driver, as a grocery-getter.
If possible, a small block is the ideal compromise, but the perfect towing vehicle will be terrible for daily driving. Anything with 4.11 rear is not fun in daily driving, even with overdrive. I mean, expect 14 MPG at best, empty, with 5.7L. It is a big heavy vehicle.
The other thing about 3/4 ton and big block is that you can always tow something about 9,000 lbs, whereas a small block doesn't give you that option.