I got mine home on my >2000# rated single-axle utility trailer (Cabell's cousin used a fork loader to get it on the trailer). Got it off the trailer by setting both brakes on the quad and skidding it down the trailer ramp with the quad's winch. I was worried about how to get it to its permanent site, but skidding it on the grass is so easy that I'll probably just drag it along with the quad, which I use basically as a small 4wd tractor.
As for trailers, the HF/Tractor Supply/Lowes/HD smallest/cheapest trailer should be fine, but be careful about tongue weight - as jbk said, the tongues tend to be too-thin square tube, and I have seen one fold a tongue up because of too much tongue weight (small load of firewood on one of these back in the '80s).
I specifically have avoided wheels or a trailer because I don't want my MEP-002A leaving home unless I want it to. We're not in a bad neighborhood, but I've seen contractor generators with the wheel kit disappear before in other places.