Granted, people are looking for different levels of quality, fancy-ness, aesthetics, and so forth. Here's what I look for.

1. Horizontal dropouts or track ends

2. Prefer steel, so I can mess around with the dropout spacing, and take care of minor alignment issues if needed

3. Avoid irreparable damage of course, such as bikes that have been obviously crashed and bent

4. A frame that comes with a usable seatpost is a benefit, since there's no standardization of seatpost sizes and it's hard to measure a frame for the correct post. Make sure that you can loosen and adjust the seatpost, because a stuck post is a nightmare

5. In general, the more usable / desirable parts on the frame, the fewer that you have to buy, at least right away. A nice cotterless crank that can be disassembled and fit with different chainrings is a plus.

6. Clearance for wider tires, if that's your preference

7. Bring a tape measure, so you can confirm the dimensions per your preferences

I believe that a lot of 1980s bikes had similar quality lugged steel frames that are good enough for building into a decent single speed bike: Schwinn, Raleigh, Fuji and the Japanese brands in general. If they weren't all made in the same factory, they might as well have been. I don't tend to look at bikes that carry a brand premium, because the sellers want too much for them. Trek comes to mind in my area.