I have a colleague who purchased on of the Chinese eBay machines, close to unusable, floppy, inaccurate and basically a total ripoff.
Look for a proprietary brand on the second hand market, be prepared to have it serviced and then you’ll be on the right track. Budget for some new pre-polish and polishing laps as what might be in the package could be worn and inaccurate so you’ll be battling on your first stone and getting very frustrated.
Good luck and be patient, the right machine will come along. Talk to lapidary clubs as well, someone might be selling or know of someone selling their machine.