I have a 2000 f250 with a 5.4 and a 5speed. I have never really towed with it, if you can find a trailer we can take it out to see how it will do.
it has 225,000 miles and is extremely reliable. It is not un-common to get 200,000-300,000 out of a 5.4L They have had issues with spark plugs coming out, the PI heads are better than the older ones (PI started in 2000, do a google search there is a "PI" stamped on the head)
The rest of the truck is solid, the interior is still great. I snagged a center console from an 02 (with cup holders, the dash cup holders launch cups all the time) The drivers seat has a little wear on it as all trucks do. The only major issue I have had is that the fuel pump died and left me standard in my garage a few years ago. It is original motor, tranny, clutch, t-case, wheel bearings, alternator, a/c still works (although doesn't blow super cold anymore and probably just needs a re-charge)
The zf 5 speed is awesome, there is a 6 speed that was an option as well. They both have a granny gear that is synchronized so you can use it to get heavy loads going and downshift into it.
We just bought a new car which means the truck has to last, when the motor goes I will seriously look at dropping a new 5.0L from an f150 into it with a standalone EEC so I can keep the 5 speed. (the new 5.0L should bolt up to the tranny, fit in the bay and will have much more power than even a re-built 5.4)
The other thing to be aware of is that around 2005, I think when they added the variable cam timing, they started using these funky spark plugs with long shanks that will rust into the head and break off when replacing spark plugs. I guess it is only an issue with the original spark plugs. It is super common and any decent mechanic will be able to take care of them, as well as many removal kits etc.
I think you should be able to stay under budget, I think kbb on mine is only like $6000.00 or something.
I know it was covered on a towing thread on hear, if you are only towing a rig to Moab a few times a year, it is worth it to put up with an under-powered truck for those few trips a year so you don't have to put up with a diesel the rest of the year...
nathan