Shockingly, I have opinions on this subject, having used everything from Unimat 1's all the way up to multi tonne CNC milling machines and laser cutters for jewelry making.
One of the things I use them for most isn't making the jewelry, it's making the tools to make the jewelry. For example: I've got a "when I get time" project to hotwire the CNC lathe that KC uses to make the saw clamps to make me a couple of extra anticlastic bracelet dies for my hydraulic press. Special forms, custom for me. You'll never see the "CNC" part of the job when you're looking at the jewelry, you'll just see the silver that was formed on the tool. So that's one thing to keep in mind when evaluating the tools you're looking at: not just "what can it do to my precious metal", but "what tools can it help me make?" Lathes in particular are incredibly useful, both directly, and as tool builders.
In terms of the lathes already mentioned, I'd look at the sherlines and taigs well before I'd look at one of the Chinese 7x12's. I've helped a couple of people try to set those up, and none of them were worth fussing with. Very crudely built.
The sherline/taig class machines are small, and light, but (A) you don't need a crane to move them, and (B) they'll do just nicely for most jewelry scale things. They also don't have a whole lot of nooks and crannies for precious metal chips to hide in, which is a unique consideration for jewelry turning. Sherline & Taig also make a very nice little milling machine, which is also quite useful.
Personally, I use a collection of antique "serious" machine tools. Several Ames instrument lathes, which look like a giant Boley watchmaker's lathe, and a couple of small benchtop milling machines, all of them from 1920-1960 or so. They're MUCH nicer machines, but unfortunately, you need to know what you're doing when hunting for machines of that class.
They can be badly broken, used to death, or missing rare (expensive) parts which won't be obvious if you don't know them ahead of time.
If you're looking for serious lathes, make sure they can take 5C collets. That's the modern standard, and was available all through the 'golden age'. The Ames machines take their own "not-quite 5C" size, and part of the reason I own 6 of them is my quest for the rare collets. Every time I found a set of collets, they came with a lathe. Don't join my club. Go with a standard (5C) size from the start. If you can find one, a Hardinge DV-59 is a spectacularly good jewelry machine.
Also, look to see if the lathe has (or can have fitted) an indexing head. This will help you divide the rotation of the headstock into controlled numbers of divisions per rotation. Intensely useful for things like eternity rings, or anything where you need a given number of holes around the rim of a ring or cylinder. The Ames (and the Craftsman/Atlas) have one built in, as does the Sherline (I think). There is also an indexing head that fits on the table of the Sherline/Taig mill, and for larger 'serious' tools, you can buy independent indexing heads that can be fitted. Very, very useful little widget.
The watchmaker class machines tended to have them built in as well.
If the chucks get worn, they can be fixed (at least enough to keep them useful) by ID grinding of the chuck jaws with the right gear, which at this scale is largely a flex shaft, some mizzy wheels, and a few bits of widgetry to hold the flex shaft in place. (Contact me directly for exact process.) But it is fixable, more-or-less. (NOT a "Hold flex shaft in hand and go after the chuck jaws" process. There's more to it.)
I guess the first thing I'd look for is a lathe. They're more forgiving, and cheaper to operate than a milling machine. For either of them, budget at least as much as you paid for the machine for extra tooling to make it useful. Typically, the tooling ends up costing at least as much as the base machine, sometimes a lot more, but with lathes you can start out small and cheap, and then work up from there as you realize what you need. Mills have some basic tooling (like vises and cutters) that are expensive right out of the gate. The good news is that you can keep a lot of the gear when you sell lathe 1, and move up to lathe 2, (etc) so eventually the tooling costs aren't so horrible. As your collection grows.
My advice would also be to buy a larger machine than you think you'll need. Bigger machines are (typically) stronger and more rigid, which makes everything go easier, as you're not fighting the capacity limits of the machine. That'll also give you some margin for making tooling, which is typically larger than the jewelry made with the tooling.
When I started out, I had the Ames, which was a 7" machine using collets (and chucks) for precious metals and delicate work, and a South Bend engine lathe, with 9" swing, using chucks, for making tooling, and things too coarse for the Ames. (The SB is for sale, if anybody around Central Ohio wants it. Contact directly.)
If you can find a good solid 9 or 10" South Bend, they're good machines, even 60 years on. The 9 & 10 inch machines tended to be workshop/garage machines, so they weren't worked to death like the larger ones were.
For advice about that sort of thing, there's another website called "Practical Machinist". Have a poke around the antique machinery forum there. There are all sorts of threads about buying/evaluating/using small old lathes and mills.
Sorry this is a bit rambling. Hope it's been useful.