AC generators are inherently simpler and more reliable than DC generators. Just a coil plus a spinning magnet. Incandescent lamps work equally well on DC, AC, or a mixture of both.
But you cannot charge a storage battery with only an AC generator, so that's why bigger bikes use DC generators. To confuse the issue further, an AC generator is often called an 'alternator,' *EXCEPT* for the one that's in your automobile. That one produces DC because it comes with a diode bridge to keep the current flowing unidirectionally.
You may find a test bulb (solder two wires to a 6v lamp) and a battery/buzzer continuity tester easier to use than the multimeter. That's because the test bulb presents a proper load to the circuit under test, while the sensitive voltmeter may show a perfectly fine voltage that you're measuring through a high-resistance defect. A continuity tester that you can hear is just handier to use if it doesn't drive you nuts with the noise.