How does one determine the type (AC v. DC) and operating voltage of small motors?
Do you have a multimeter? Easiest way would be to probe the motor while it's running in its original circuit. Aside from that, if it truly is unmarked then it'll be tough to tell. I believe DC motors typically have only 2 wires, some AC motors have more wires for additional phases. I'm not an expert on the different types of motors, but searching your question yielded this thread, which seems to have a lot of relevant info.

The safest way is the buy a motor with corresponding specs so you know exactly how to drive it. Alternatively, the method mentioned in that other thread of slowly ramping DC voltage to see if it works may also suit your needs.