Some advice from someone who has been there, done that.
You have started off well by coming to the forum to read and post questions.
Don’t fall into the “its an 8 cylinder it can tow” anything mind set. Tow capacity is more than the engine size, there is also; gear ratio in the axle, transmission, suspension cooling and breaking to consider in towing. People on here have towed with a small block V8 like a 5.3, but, most prefer the 5.7 or larger. The tow vehicle will list a “gear ratio” like 355 or 410. The higher the number the more torque to the wheels and more the vehicle can tow (lower MPG), and of course a ¾ ton or 1 ton truck is built heavier which includes things like suspension, breaks cooling.
Some will tell you that a 1 ton dually is needed to tow a pop-up, so be careful of that mindset also.
So before your head starts spinning, most auto-makers have an area that list lowing capacity for their trucks,
here Is the web site for my Dodge as an example. It tells me what the maximum trail weight I can SAFELY tow. Can you tow beyond that? Sure but not safely, you will not like it and your insurance company may have issues should you file a claim from an accident.
I bought my Dodge Ram used and there are many nice used trucks out there that people are selling or getting rid of because of the price of fuel. Keep in mind that towing is rough on a vehicle; the engine and transmission run hotter and work harder. If the used vehicle is at the end of its life, walk away and keep looking. BTW car dealers will lie about the towing ability to make a sale do your own research.
When it comes to the travel trailer, keep in mind this will be your first but not your last trailer. You will upgrade and that will most likely mean a heavier trailer.
So here is my “been there done that” history. We wanted to move up from tenting to an RV, and were looking at Pop-ups. We knew our 1995 Ford Windstar (POS) would not tow well and wanted a tow vehicle. My buddy’s brother in-law worked at a car dealer and found a 1990 Chevy low-top conversation van. He said it had a 350 V8 and could tow anything. It was nice inside and only had 125000 miles on it. I bought it and had a hitch put on. We went to an RV show and DW found a Hybrid Trailer she like more than a pop-up. I did my research and found I could tow 5000 lbs if I added a tranny cooler (bummer). We did order trailer with a GVWR of 4800 lbs, this was not our first choice in floor plans and was a mistake. So here is what we learned; we could not go very fast up hills even on the interstate we would be so slow we had our 4 way flashers on, the engine temperature would raise very high on an incline. We constantly had to worry about cargo to lighten the load, we always had to plan trip around hills. About 2 years later we needed to replace the van and bought our current Dodge Truck, WOW what a difference it made towing! I would forget the trailer was there, no problems on hills or worrying about cargo. However, the original HTT was smaller than we actually should have bought with 3 kids (should have bought the one I originally wanted but had to pass because I couldn’t tow it) Our younger children slept together on the rear bed and our oldest on the sofa. It became “icky” for my son and daughter to sleep together and 5 years after the purchase it was time to find a different layout. RV depreciate quick and at trade in I was given 50% what I paid for the trailer. And yes the new trailer is slightly bigger by 2½ feet but 2000 lbs heavier.
So the lesson is to “Be Patient” find the right combination tow vehicle and the right trailer for your family. If you settle for less than that just to start RVing you will be making changes and those changes will cost money. Don’t be too scared to act either. Sit down with DW and make a list of what you NEED and what would be nice to have in the trailer. (I would not ask the children). This list is your reality check when you go shopping.
Things to think about: fresh water capacity, black and gray water capacity, bunk length (some are short), storage capacity, ease of reaching the dump handles,
Hope this helps…..