Sherman: I'm definitely going to use a more robust palette for later stuff, I just thought EGA would be an interesting place to start. I wouldn't want to paint my walls these colors, but it's fun to see what I can get out of them.
eck: Good point. I'm fiddling with the colors right now. Thanks for the edit!
The EGA palette restrictions seem to be any 16 colors out of a preset palette of 64 - according to Wikipedia of course. No other restrictions were mentioned.
I'm using the default, eye-burning set of 16 colors.