Are you looking at a manufactured home or a trailer (mobile home)? If , as it sounds from your post, you have a 1960s trailer for sale for $20k in a trailer park, then it's overpriced by roughly $18k, maybe more.
Potential other issues: if it's in a park, are you buying the lot, too, or just the trailer? If it's just the trailer, you'll still have monthly rent on the lot. If it goes up or you don't pay it, you may have the option to move elsewhere, but it may be structurally unfit for moving, and it may be illegal to make a trailer of that age on public roads. Plus it may be illegal to site a trailer of that age anywhere nearby. Also the lot owner may be able to seize the trailer for back rent. So find out about lot rent.
I did convince my husband to live in a trailer of about that age (1971) for what ended up being four years, up until last summer. But it wasn't in a park (the trailer was already on the acreage we bought to build on). Still it took some considerable convincing. Neither of us is sorry now in retrospect, but that's not because of getting cheap housing out of the deal; it's because we got our dream house out of the deal. We actually got a small discount on the land purchase because of the expense we'd have to incur in removing the trailer.
In other words, there are a couple of ways this could go well, but there are many, many ways it could go very badly, even without bringing up the issue of living in a park. Proceed with extreme caution.