Please note that I'm still something of a beginner at 3D printing, so this guidance is probably rather incomplete and may even be misleading or wrong in parts.
Most all the really inexpensive printers tend to require more or less fiddling and tweaking to get working well--fine if you're looking at a hobby, not so great if you're looking for a tool that you can
plug in and use. (A fair few are kits that require assembly, for that matter.) Particularly with these lower-end machines, I think it's a good idea for beginners to get a popular model as there will be more readily available help from forum posts,
etc. when things aren't working quite right, and to figure out the best ways to fix design flaws or limitations that really probably ought to have been right from the factory. In some respects they're sort of like some Harbor Freight tools; it may take a
bit of re-engineering to make something really useful.
In terms of specific features to look for, there's rather obviously
build volume (how big a thing you can make at once). Beyond that are some things that affect what all materials you can reasonably print with. The
current "standard" plastic is PLA, which is easy to use, doesn't give off much in the way of fumes when printing, is pretty inexpensive, and is reasonably strong although brittle. It does not handle elevated temperatures too well--PLA parts would tend to get soft and maybe droopy in a hot parked car, for instance--and has a tendency to creep a
bit over time when under stress, which among other things means screws threaded directly into the plastic tend to self-loosen over time. While it's possible to print PLA without a heated bed, nearly all other materials require one, and most also require a hot end that can reach higher temperatures (an all-metal hot end) and possibly an enclosure to hold the heat in. Some pretty much need ventilation outside or at least through a decent filter due to icky fumes. For printing flexible materials (with rubber-like consistency), a direct-drive extruder is helpful.
That's all about FDM machines. There's another entire class of machines that are based around UV-curing resin rather than squirting out melted plastic. (There are a few other technologies around as well, but they're in the tens or hundreds of thousands of dollar range.) The resin is kind of nasty smelly stuff, a sensitizer similar to
epoxy, and cleaning up the finished prints can be a
bit of a messy operation. The resin is also comparatively expensive. The big advantage the resin printers have is that they can produce very nicely detailed prints, and do so at comparatively quick speeds. There are some resins available that can be used as matrixes for metal casting using lost-wax equipment and techniques, if I'm not mistaken, which is a neat way of making such things as rings or charms.