It all depends on what you want to tow, for how long at a time and if it is also going to be a daily driver.
The later the model, and the lower K's the better. Try and find one that hasn't been fiddled with.
Cabins are usually pretty rust free but they will go behind the guard brackets and bottoms of doors. If the windscreen leaks then have a look under the floor mats. Some, usually ambulances may have the front of the cab galvanised.
Check for signs of accident damage, run a tape measure over it to make sure the chassis is square, Bent bodies are easy to fix, bent chassis are a big pain. Towing with a vehicle that crabs is not a happy experience.
Mechanically F trucks are Fords version of a mechano set. Easy to do anything on them, as long as your strong and have the time. They're pretty good though. Any whine from the gear box (manual) is $$$ and mucho agro. A well looked after cleavo either 302 or 351 will haul just about anything you want. Steer clear of the 6's as aside from being thirsty they're slow as a wet week.
As for LPG a good Impco gas kit will be no problem, but Dual fuel is preferable cos F trucks are too heavy to push.
The I beam front end is pretty fuss free, Any klunks are usually worn shocky rubbers, though worn I beam bushes or radius arm bushes can also be the culprit. Check the King pins for wear. None of this is unrepairable but its heavy dirty work.
Brakes in 73 and later are Disk front / drum rear, note F100,250,350 brakes are not interchangeble they are unique to each model no major dramas and they usually work well.
Earlier than 73 trucks are drum all round and can be chore to maintain. You can upgrade them but it means changing front ends, much $$$ and agro. Biggest woe for all models is the master cylinder leaking, not a huge problem.
The F100 ex Ambulances are pretty good value in that they are a van with lots of storage for nick nacks and usually C6 Auto. They make good work/camping wagons and are usually on a long wheel base which is good for towing. Ex Ambo's usually tare around 1.5 Tonnes with around another tonne worth of payload to give a GVM of 2.5 Tonnes. They usually have a version of the 9" diff
Unless you really want 4X4 then steer clear, be it a Bronco or F250 4X4. Its not that they're bad but if your on the road all the time then it'll cost you extra $$$ in tyres and fuel.
F350's come in short, mid and long wheel base and they're rated to 4.9 Tonnes GVM they run a 4:11 Dana 70 floating diff and 16"split rims with duals on the rear. I've never seen one with an auto. They are the most truck like of the breed, and to own one you need to think like a truck owner/driver. You must keep the rear wheel nuts tight or you will snap all the studs off. Happened to me, Bastard of a job to do on the side of the road.
Think of a F250 as a uprated F100 with about an extra half tonne of GVM. They run a smaller Dana 60 full floating rear diff with 16" single rear wheels. Although I have seen some with the bigger Dually Dana diff.
F trucks usually keep their value because they're such durable beasts. I've owned a few of them and if I had the need would buy another one. Usual caveats apply when buying second hand and if you don't know what to look for find someone who does to help you.
If your going to tow a 2 horse float or a car on a trailer, or perhaps a Ski Boat/Fishing boat then you should look to an Ex Ambulance as they're the most practicle.
If your going to tow something much bigger perhaps with a fifth wheel then a F350 is the go
Hope this gives you a start. The tonnages I've quoted are off the top of my scone from a memory of having had the workshop manual in my hand once upon a time. They should be close but.