My first reaction was that you don't have a big enuff TV to be able to tow a TT that will comfortably fit your family.
Also reminded me that I was in the same position as you when we started RV'ing in 1987. Got tired of tenting in the rain (Pacific NW) with 3 kids. Bought a well used 1973 19' Prowler, turned out neither our 1965 Chevy Van nor our 1978 Aspen Station wagon would pull it. So, had a 292 6 cyl engine, TH350 trans installed in the Van and towed with it 90,000 miles since, usually 24' TT's. (Took it all the way back to Mt. Rushmore and down to Disneyland) So, we made the age old mistake, bought the TT before thinking about what the TV could tow.
Recently made the same mistake 29 years later (will I ever learn?). After towing our 4300 lb 2004 22' Tahoe Lite to Bend OR last year in 100 degree temps with the van that has no A/C, we realized it was time to upgrade the TV, one with A/C.
At the time I thought the Tahoe weighed less than 3500 lb loaded (shoulda weighed it first), and since we wanted to have a smallish TV so wife could drive it around, in December we bought a 2004 Envoy with the 4.2 6 ci, 3.42 gears. Much to my surprise the Envoy (a loaded w/every option 4x4 cream puff) weighs 5000 lbs. The max tow rating is 5,000 lbs and total combined vehicle weight is 10,000 lbs. So we were almost at max rating right off the bat. Did tow a couple of times and it was just "ok" but really struggled up 6% Stevens Pass (2nd gear, 4,000 rpm at 53 mph).
So, had to jump back on the internet for next 3 months until we finally found a cream puff low mileage super clean 1994 GMC Suburban 1500 with 350 engine. Has tow package. It's rated to tow 7500 lbs, so it does the job. It is a half ton but so was the Chevy Van. 1/2 tons usually have a higher tow rating than similarly equipped 3/4 tons since they are lighter. It has no trouble towing the 4300 lb TT.
I think if your TT gets above 5,000-6.000 lbs unloaded, you should get a 3/4 ton truck with a larger engine than the 5.0. My old 292 6 cylinder van would out pull that, got to have a lot of torque to get the massive weight started. Those little V-8's rely on high rpm's to develop power which stresses the engine and transmission a lot. When we had a 30' Arctic Fox we towed it with a 1988 454 3/4 ton Suburban.
Oh yeah, I also recommend the Equal-I-zer hitch, takes all of the sway and therefore most of the fear out of towing. Used them for years.
Welcome to the club and I hope you find something that will fit all your needs and will be SAFE hauling your precious cargo around. You can't be safe and protect your family if you cut corners.
It's a good idea to listen to us old timers who are still around, we've apparently done something right, or have been very lucky, or both.
1994 GMC Suburban K1500
2005 Trail Cruiser TC26QBC
1965 CHEVY VAN, 292 "Big Block 6" (will still tow)
2008 HHR
L(Larry)V(Vicki)J(Jennifer)J(Jesse)J(Jason)