Alright, let me tell you about myself. First the diesel trucks I have had over the years. 84 F250 IDI, 94 F250 PSD, 01 Chevy 2500 Dmax, and currently 84 F250 IDI.
I was a Ford diesel master in 2007, and am currently a Navistar tech, I do mostly engine work if I can help it.
the 6.0s caught a bad rep to quickly, and IMO they are better motors then the 6.4s. I have done many repairs on a 6.0 truck, and have never once had to remove the cab, there are tricks.
I think the best year for the 6.0 was the first year, they seem to have held up the best. The 6 speed trucks drive like crap when they arent broken, you just cant seem to shift them right, witch is odd, because the 7.3 super duty 6speed trucks shift so sweet.
I would recommend with your price point, and expectations out of the truck, for a 03-04 6.0 truck, parts arent to crazy priced, they held together well, the transmissions are good units, and generally speaking, you would have on your hands a solid truck.
Thats just my opinion, you can pick up the 6.0 trucks for cheap because they have such a bad rep, but they are good trucks, with a few issues. People also had such a bad time with dealers fixing them incorrectly, put a general bad taste in the mouths of some owners.