eBay probably won't be necessary to get your hands on DVD-R media. You can probably pick it up the same place you purchased the CD-RW media. DVD-R media does cost significantly more, though.
Look on your DVD player for "Video CD" compatibility. Remember, though, that if even though the DVD player claims compatibility with Video CDs, not all burnable media will work in it. Some DVD players are picky, and don't like CD-RW media... accepting only CD-R media. Others don't like burned media, period. Still others work well with certain brands of media, while rejecting other brands, even though they all carry the same "CD-R" or "DVD-R" moniker.
It's just a hit-and-miss kinda thing now. I've discovered that my Sony DVD player likes both Apple- and Verbatim-branded DVD-R media, and doesn't like Memorex (frequently showing pixellation/blocks during playback). No matter what I try with VideoCDs, it just doesn't like them at all even though it claims compatibility with them. Haven't gotten one to play yet, even though they play fine on the computer.
Also bear in mind that VideoCD quality is on par with VHS quality, and is far, far below the quality you'd get with a true DVD. The quality also depends on the quality of the source media -- in your case, the AVI or MOV file. If the original media looks bad, making a DVD or a VideoCD out of it isn't going to make it look better.
Good luck with it, and feel free to ask anything else you need help with!