>>796723$1k is going to be a challenge for any liveable trailer. You might find one for $1k, but it'll likely need at least that in parts&repairs.
Wherever there's an exterior door, window, cabinet, vent, etc, there's a seal. That seal ideally keeps water from getting inside. Over time those seals dry out, rot, and crack which lets water in.
If it's sat for a while in the elements, check for mold or rot under the interior panels around doors/windows.
A $1000 trailer may need all new seals, possibly mold remediation.
Wiring in trailers generally sucks. They start shitty from the factory (wired well enough to make it legal and get it sold/out the door). When something breaks, it's usually fixed cheap/quick, not fixed the right way.
When I went through my trailer, every inch of factory wiring came out and got replaced with decent parts. Turns/markers/brakes, brake wiring on the axles, 12v aux. Also installed a 120v circuit, which was entirely worth the effort.
Same deal with the trailer i'm working on now - pulled about 1/4-mile of wire through it, and there's still another 200-300ft to go (Marker lights, taillights, utility lights on the sides).
With a single-axle, you want to make damn sure your wheels/hubs/axle is in good condition. It's a lot more important than a two- or three-axle trailer. If the brakes lock up and you lose a wheel with one axle, the trailer's parked where it broke till its fixed... with multi-axles, you can usually limp to a parts store and fix it there.
They're not hard to maintain... bearings need to be greased and brakes should be adjusted seasonally, seals and lug nut torque should be checked periodically, tire pressures and condition before each trip.
Towing's also harder on the tow vehicle - transmission, cooling system, and brakes are usually what causes problems. There's a reason I traded in my half-ton for a 3/4-ton heavy-duty pickup.
Currently working on my 3rd trailer build, biggest one i've done so far.
