Trailers are an excellent option, by far the best bang for your buck; I'd have one if I didn't need to pull a big flatbed trailer to carry my M/V.
You can get a bigger, nicer trailer for cheaper than any other type of RV, and you have no extra truck engine, transmission etc. to maintain. (Assuming you already have something to pull it with.)
First of all - get a weight-distributing hitch! Those are the expensive ones with the extra "spring bars" that attach to the trailer tongue a few feet back from the hitch ball. You absolutely need that, the difference in stability on the highway is huge.
You check out a used one the same way as others, try all the appliances, etc. The refrigerator is the only really important one, because RV fridges are very expensive. I once bought an old motorhome I didn't want just because it had a new fridge in it.
If an RV fridge has an ammonia smell, consider it junk; when they start leaking their ammonia, they are not gonna be a cheap fix.
I've seen a lot of used RV sellers claiming the fridge "needs a recharge". They don't know what they're talking about, if you hear that, consider the fridge junk.
Often a perfectly good RV fridge isn't working just because it sat too long and crystals form in the coils on the back. Frequently if you open up the access panel behind and whack the metal tubes with a block of wood a few times, it will start working again.
The rest of the appliances are somewhat important bit not as big a deal and not as expensive to fix. Make sure the water heater doesn't leak, they tend to rust out over time.
About the propane bottles: they are good for 12 years, then they need to be recertified - then every 5 years after that. If the rig is 12 years old or more, look at the date stamped in the bottles, propane refilling stations aren't allowed to fill them unless they're current.
I'd advise against any single-axle trailer because they sway a lot more than two-axle trailers.
Make sure the tires aren't too old, on your way to BRC tread wear isn't what gets you, it's old, cracked, dried-out sidewalls. That's why you see people putting covers or even pieces of plywood over their RV tires when parked.
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Delle: Singularly we may be dysfunctional misfits, but together we're magic.