Why not do what the pros do, and get a van instead of a trailer?
Something the size of a Ford Transit should fit what you describe, no towing required, and these days they have reasonable cabs. Also, in many ways more flexible than a truck, since the loading area is much lower and covered.
The naked ones (i.e. no passenger seating) should also be pretty affordable. (30k new) You could even tow your luggage in a smaller trailer, should the need arise (i.e. picking SWB/short model so you have a more reasonable daily driver)
Either that, or a decent trailer with a reaction brake. With that almost any car will do, but something with a low-range manual gear box will be best. Diesel certainly makes things the easiest, and a Diesel turbo V6/I4 may well run cheaper than an Otto-engined car with similar torque.
Those SAV/sub-SUVs are probably the most interesting class of cars to look at (since VW was mentioned in the previous post: Tiguan could be an option) since they're somewhat marketed towards that kind of niche. In the end though, low end torque is what makes driving the trailer easy (both on you and on the clutch/transmission) and that's something that the sporty aspirations of that class often ruin.
My protip: Rent a Transit first, if you like it, buy one and mod it into a driving workshop. Camping equipment optional