Matt - what you need to find out first is if your DVD player supports DivX playback.

Burn the AVI you have to either CD or DVD as a DATA DISC using nero. Then just put the disc in the DVD player and see if it will read and play the AVI. Some do, some don't....

If that doesn't work, then you don't have DivX support on your player, and you will need to encode to a different format to get it to play.

VCD is shit - I used to encode video clips and the like the VCD using Nero but the quality is just shocking - nothing like the KVCD's you can get hold of on the net

You are best off converting to DVD format using an AVI to DVD converter or Nero Vision Express as Hock says. Get yourself a DVD-RW disc and you can burn stuff, watch it, then erase the disc to reuse it again next time - is what I do