Welcome to the Forum!!
There are several comments here, in no particular order.
You should be okay with a PROPERLY EQUIPPED ? ton pickup truck with max tow package. The key is how much weight the truck is designed to carry (payload). This includes all passengers, cargo in the truck, 80# for a Weight Distributing (WD) hitch and the hitch wt of the camper, or 10% of LOADED trailer weight. However, if you have a cap on the truck and store 1,000# of "stuff" in the truck, then this weight counts, too, and you will need a ? ton truck.
NEVER use the UVW of the truck to determine how much you are towing. It is probably heavier than that when it left the factory, and likely does not include propane tanks, needed hookup stuff, or anything you will carry in the camper. The GVWR is a much better estimate of the weight when you tow it. In this case, 9950#.
You indicate you are a bit tight in money, so why a NEW camper? A gently used camper will cost less. New entry level campers all have factory "oops" that will be repaired under warranty, but we are talking about taking your HOUSE to the shop for a few days - or weeks! Where will you live?? A gently used camper should have these issues resolved. If you decide you want a different floor plan or need a bigger camper in a year, the trade will be much more affordable if the trade is purchased used. It also leaves a bit more flexibility on the price of a truck.
Where do you plan to camp? No camper is a good place to spend the winter in a cool climate. How long will you stay in one place? How will you produce income while traveling?
For the truck, a ? ton or 1 ton SRW will be your best bet. The TT (travel trailer) can only carry 2000# of stuff, so I am sure the truck will be carrying the rest of your necessities. If you are towing the TT over 10,000 miles a year you may prefer a diesel, especially if this is in the mountains. The big issue is diesels are more expensive to buy and maintain. Gas will be more in your price range. For the bigger trucks, you usually have two motor choices - one gas and one diesel. That choice makes the transmission choice for you on most models. You will want the tow package, if not standard, and that will bring a strong suspension.
I hope this raises many more questions. ASK AWAY!! If you do not know the answer, it is not a dumb question.
Read lots of threads and Library articles (tab near top of page) and you will find answers to many questions and ease some of your fears.