Congratulations and good luck in your search. You should have plenty of tow vehicle with an F-350, but your big decision will be gearing and what type of hitch set up you want. Others can provide guidance on the gearing, but my vote for the hitch is the B&W Companion. It can fit into the puck system on the Ford trucks if installed and best of all if you want to remove the hitch you can and will have no rails in the bed of the truck.
As for the 5th wheel we just went form a 34'TT to a 39' Toy Hauler 5th wheel. The first thing you will need to pay attention to is the turns. A 5th wheel will track to the inside of your turn so you do have to swing a little wider especially on right hand turns. It is not bad though and after a few times towing you will easily have it down. I love towing our 5th wheel as it is much more stable than our TT was.
As for the height I have not had any issues so far and most of the time you will not either. What you will find however is that the interstates will be no issue, but the side roads, back roads, etc. is where you may run into some issues. A good RV GPS can help with this, but will not catch everything that is a low clearance. I have more concerns with overhanging tree limbs.
The length will cause you to be a little more selective with campgrounds, but most of the more modern campgrounds accomodate larger units than yours. Now state and local park campgounds may be another story. We are limited on some of the state campgrounds in Georgia due to our length.
Just my feedback. This forum has a lot of knowledgable people that will be glad to help you along the way.