18K minimum.
Hitch can be moved to NEW truck when you get one and it will be less expensive NOW vs 8 yrs from now.
Your current truck MAX Tow Rating of 14,500# is on paper
You will be pushing limits of truck even with trailer empty at 13,500# and dry pin weight of 2735#....which is probably TWICE what your cargo capacity is!!!
Especially since your current truck is a 2002 F250 which in the real world of towing is maxed out at 12,000# 5th wheel
Your Trucks GVWR is only 8800#.
In essence.....your truck is not the right tow vehicle to be used even with 5th wheel empty