Welcome to the JOF Jess! As you may have figured out most folks on this forum are Jayco fans (myself included).
It's been pointed out that the tow limits on your vehicle will be the limiting factor and as pointed out a Pop Up would probably be your best choice and would give you better mileage than a hard-side TT. I've not owned a pop-up so I can't speak to ease of use (or the lack of) but you sound like a pretty competent and self-sufficient person so I doubt you would have any trouble that you can't overcome. If you have any outings planned in the near future watch for a PUP getting ready to set up or knock down, wander over and ask to watch (and ask questions). In general I find trailer folks to be very helpful.
Regarding the TV and its weight, the yellow sticker on the TT will tell you what it weighs when empty (no water, battery or propane). It will also tell you what the max weight of the TT and "stuff" can be. Let's say it weighs 2000# empty and has a GVWR of 2800#. That means that you can load 800# of "stuff" (don't forget the battery...) before overloading your TT. The weight on the tongue of the trailer should be about 15% of the trailer weight so in my example about 420# (I'm assuming it's loaded to the max). Not only do you need to consider the tow rating of your vehicle (3500#) but also how much weight is on the axles. The yellow sticker on your TV will tell you that (Front/Rear GAWR). Unfortunately the only way to know what each axle weights is to visit a scale and get your vehicle weighed (the CAT scale costs about $10 and you find them at truck stops). You will then know if you can safely add that additional 420# to the rear axle.
I hope all of the posts are not overwhelming but helpful. I posted MANY questions prior to our first TT purchase and always found helpful responses. There is a very detailed set of instructions on weighing your TV & TT here: How to Weigh...
Good luck with your adventure and keep posting your questions!
Oh, in case you don't know:
GVWR = Gross Vehicle Weight Rating
GAWR = Gross Axle Weight Rating
2013 F-350 CC SB 2WD 6.7PS
2013 Eagle Premier 351 RLTS
-SOLD- 2012 X23B
-SOLD- 2003 Ford Expedition 5.4, Bilstein shocks