For multi-day stays on the beach you will need the biggest holding tanks you can find. This will mean getting a camper on the larger end of the spectrum as the ones that will work on an F150 have tiny tanks. I would say go with an F350SRW as it will drive the same and is no bigger then an F250 but with increased load capacity.
Air down right before you leave the pavement onto the beach. It can take a few trips to learn what air pressures work for you in each situation. Don't be afraid to go lower then you would think given your load. It's safe as long as you drive slow, avoid sudden turns and air up IMMEDIATELY upon reaching pavement again. A quality air compressor is a must.
If you aren't planning on any mountain travel then a gasser will work ok.