I wrote this
What Can I Tow? page specifically for my father-in-law who was asking the same question.
Basically, you have to ignore GCWR as you'll likely never hit it with a F150. Your biggest limiting factor is how much the F150 can carry (you, your wife, your stuff, your hitch and pin or tongue weight).
Once you find your actual available payload, you can then do the math to find the trailers that you can safely handle. Typically, you can have a larger travel trailer than fifth wheel because TT's have 10%-15% tongue weight where as fifth wheels have 15%-25% pin weight.