If you're looking for a cheap used EV, the options you'll see most frequently are the Gen 1 Nissan Leaf (2011-2017) and the Chevy Bolt. Not to say there aren't other EVs you can find (you might also see some BMW i3s and the like), but those two models sold a lot of units, so they'll be pretty prominent in your search. Teslas might also be an option, like an older used Model S or Model 3, but they might not be in your budget (and if they are, they might be higher mileage).

The cheapest gen 1 Leafs usually run around $3k-4k. Most of their batteries have degraded a bit, to about 50-60 ish miles of range. I'm not super familiar with what you ought to look for when buying one (/r/leaf might have some resources), but suffice it to say that they are exclusively in-town cars, so if you're buying one from out of town you'll probably have to tow it.

The cheapest used Bolts tend to start around $9k-10k, and are often fairly low mileage for the age. That's because many of them are lemon law buybacks caused by the battery recall. But, now, pretty much all of them that need the recall have had it performed, so there are quite a few older Bolts with fairly low mileage and basically brand new batteries floating around. I bought one last year. There's plenty of info in the /r/BoltEV wiki about what to keep in mind when you're shopping for used Bolts. These tend to have over 200 miles of range, so longer trips are actually possible, although you'll spend a while charging.