The F250 will do the job. Might need air bags. Will be safe.
But there is little or no reason to buy an F250 instead of an F350. The F350 costs almost nothing extra if you compare it to an F250 with camper rating or snow plow option, which you would definitely want. The two trucks ride the same. Not like the lumber wagon riding F350 of years past. Progressive spring designs have made them ride very well. The only possible negative to an F350 is a little higher registration weight fees, depending on where you live, and a few areas in the country where trucks with GVWR over 10k are restricted from travel or parking. I'm told some areas of New York for example are restricted.
Unless those restrictions apply to you, it is rather silly to go with an F250. But it can be harder to find the F350 you want, and you might have to order it to get your ideal truck.