Late to the party, but here's my two cents if you want to go the old machine route...
1. Is it from the 1940's/50's?
This will usually indicate all metal, well-made machines. Going for too old (20's or 30's) of a machine might mean headaches with wiring, rusting, etc. Singers are tricky, because they all kinda look the same and a lot aren't marked with a model number except by serial number lookup process. Taking a few seconds to familiarize yourself with the markers between a 20's Singer and a 50's Singer could save yourself a lot of trouble and land a great deal.
2. Is it straight stitch/zig-zag or does it have a lot of bells and whistles?
The more junk (embroidery, etc.) the harder it will be to maintain and tune. An example would be the Pfaff 130 vs 230. The 230 is a very similar machine to former with the addition of an embroidery unit that is a pain (at least for me) to tune.
3. Can you find a service manual & owner's manual online?
This is the primary reason why I would avoid lesser known machines. I think quality is great on a lot of the random branded machines out there, but I know I can find manuals for a Pfaff, Necchi, Singer, etc so I would stick to those.
4. Will it take a while to get the machine useable?
Projects like rewiring, painting, or DIY servicing add both time and money to a seemingly great deal. In my opinion, a paint job is not worth it (coming from someone who has both painted machines and had them powder coated). I would pay $50-100 more for a machine with a paint job that's in good shape so I don't get the DIY paint bug again and feel like I have to spruce it up.
All that said, a couple machines I would keep an eye out for are the Singer 201-2 or 15-91, Necchi BU, or a Pfaff 130, which are all either straight stitch or straight stitch/zig-zag. There's lots of other machines out there, but these definitely fit the bill. I have a 15-91 and its simplicity (straight stitch only + reverse) removes a lot of distractions and allows me to focus on sewing. Or typing great walls of text on forums.