There's nothing wrong with getting the vehicle first, but the camper dimensions do vary between brands. If you look at an Arctic Fox, the floor starts above the wheel wells and has sub-wings about 6' wide while a Host starts the floor above the bed rails at 8' wide and the lower section is only 4' wide. If you start with a flat bed and only provision the underside boxes until you get the camper, you leave all options open (even a custom flatbed model Northstar). Start enclosing the sides, and you find you have limited your camper choice or you have make an expensive redo.
I would not go to a utility bed until the camper is purchased because of the variations between brands. There are upfitters that install pickup beds on the chassis cabs - You could go this route if you want your F550 to look more pickup than commercial. It would give you flexibility to use any camper other than a flatbed model, but you loose the storage potential of a flatbed or utility body.
192" wheelbase means you are looking at 84" CA model trucks that have an 11-12' deck. You will only be able to get 8-9' of the camper on the deck due to protrusions under the rear wings for stairs, drains and generator exhaust. You either need to plan on forward storage box or modification of the camper or deck to accommodate those protrusions. My 5500 is a 60" CA model with crew cab giving me a 173" wheelbase. This is slighly longer than typical DRW CC 3500, but it still turns sharper due to the wide front axle and deeper wheel wells.
My previous truck was a short bed extended cab. I really do not have the need for the crew cab but did need some room for a kennel, so a standard cab was out. Ram does not offer their extended cab in these trucks, so I had to go to the larger crew size. If I had chosen the F550, It would have been the Super Cab with a 60" CA frame.
Think about what you may tow behind your truck camper. Even chassis cab receivers get derated quickly with an extension, so you need to look at a custom placed receiver mount on extended frame rails or a way to incorporate a SuperHitch so you can use a double truss extension like the SuperTruss.
Host Mammoth 11.5 on Ram 5500 HD