Just for syncing, really the internal mic is not bad. I actually used some of the sound from one to blend into foley.
That said, if you want some safety, the Audio-Technica Pro-24CM runs about $70 online and is stereo. Gets decent reviews. Stepping it up, you can go for the Rode VideoMic at $150. The A-T runs off of LR-44 batteries (cost about $1 each) and the Rode runs off of 9V.
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If you're shooting with anything at about 80mm or closer the internal mic will work great. I just finished shooting a doc almost entirely with a 50mm lens and a 38mm lens (under a highway) and have been able to sync everything pretty well, though I'm doing it manually since I don't own plural eyes yet.
between 50 to 120mm glass or so a camera mount shotgun can help, but noise may still affect the quality of what plural eyes can do.
Once you get out really long no shotgun will help you, and you'll have to take a wireless feed in.