There is no end to the variety of trailers out there. I would start with what vehicle you already own and then search what U-Haul sez. Check that against the vehicle manufacturers guidelines (can take some searching).
All too many cars with MORE than adequate brakes & power are under-rated, due, mainly, to the lack of testing by the manufacturer. The new SAE J2807 standard on towing does not address this shortcoming, although the test is rigorous: includes power to back up a ramp, power to take a VERY long steep grade, etc, etc. But the test precludes trailer types, etc. Chances are, in other words, that your Honda Accord can actually handle a decent trailer if:
tires/wheels are sufficient
a weight distributing hitch is installed with a custom hitch receiver
Auto trans cooler
power steering cooler
Etc etc
Not for the unskilled nor for those unwilling to pay for experiments. So see if you can find out what the vehicle is rated for overseas. But, as you do so, remember that European trailers meet a different set of safety standards. American trailers rely on a high tongue weight percentage (10-15% of trailer weight) and some European trailers are set up for 5-7% TW. It's easier for a smaller vehicle to deal with less TW.
Trailer stability (anti-yaw) is handled, when necessary, with add-on equipment. Braking is also thru surge style brakes versus American style electric brakes. Frankly, as in so many other areas, as the US declines into Third World irrelevancy, the civilized world changes standards to meet new information and studies. We get the poor cousin treatment, here, and are stuck in the 1960's on too many items.
A short wheel base vehicle such as a Wrangler can be a more than decent tow vehicle provided it is set up properly, and reasonable limits maintained. My Cherokee is capable of 5k and a fair frontal area on the trailer. In all cases, very low center of gravity, wide-stance roll center (torsion/independent axle) and electric over hydraulic disc brakes is always superior. As is the sway-eliminating PRO PRIDE hitch (and two others). Not cheap to set up, but it can all be done.
As to what is the most useful trailer my vote goes for a dump trailer. One can increase the wall height and install a cover, and otherwise cover every contingency a homeowner might need. But these trailers are usually of a fair size. The nicest one I have seen is, no surprise, European (and sold here).
THULE 3-Way trailer
Thule Three Way Tipper Trailer - Four Wheeler Magazine
BRENDERUP is a manufacturer of horse trailers in Europe and now imports here. This is a low TW, aero trailer that a fairly small SUV/truck can pull with ease.
Brenderup Real Trailers
Plus, there are all sorts of kits out there. Any car I owned I believe I could come up with a satisfactory trailer to make a cross-country trip. Might be slow across the Rockies, but I'd get there. And the tow vehicle would be find afterwards. With this goal in mind one ought to be able to find something suitable to work your metro region.
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