You don't mention diesel or gas as preference. For full time use, a 2011 or newer F350 diesel is the obvious choice, even with the mid sized FW. In this case warranty would be important. If you'd rather go gas, then a 250 will work. The 6.2 with 6-speed will handle that trailer with either available gear set, the 4.30 being best for full time, but much harder to find used. The FW prep option would be nice.
The warranty would not be as big an issue with the 6.2 gas.
If you find a great deal on a 250 diesel, it will work fine, depending on suspension package, or air bags can be added if needed, for a larger trailer, than the one you are looking at.
Jerry