Enjoy the new TT! You will love towing with the F250 SD. :)
Check the suspension & tires. Look for worn shackles & bushings and for anything that doesn't look right. Do a bearing inspection, clean them, repack & new seals. Check brakes. Replace tires (need to be correct load range). I would spend a few hundred $$ or so and take it to a good frame & axle shop for inspection and bearings/brakes. That may save you a lot of grief and expense down the road.
Specs say GVWR is 9450 lbs. Dry tongue weight is listed as 650 lbs. The actual tongue wt. will likely be around 1100 lbs, possibly a bit higher. Make sure the WDH is rated for that - probably 1200 lb spring bars. Learn how to properly set up the WDH for safety, handling and sway reasons. There is a good sticky on this. You'll most likely want to add friction sway control to the WDH (if not provided). If you find sway is an issue, there are some good WDHs to upgrade to like Reese dual cam, Equal-i-zer and a couple of others with integral sway control.
If you're not familiar with a TT and everything in one, it might be a good idea to take it to a local RV shop (independent) for an overall inspection & report - 12 volt system, propane system, plumbing systems (waste and water) and holding tanks, etc. You don't have to pay them for anything that may need doing if you can do it yourself. They know what to look for and again, may save some grief and $$ down the road.
And most definitely check for leaks and re-caulk as needed. Water leakage can be the kiss of death in an RV if ignored.