Crank Bros eggbeaters are what I ride, and these may be the mostly widely used in CX. Simply, no adjustments, and you enter on four sides.

Moo

Crank Bros Candys or Eggbeaters, Shimano SPD, or Time ATAC pedals are what 99% of the population uses for 'cross. Essentially what you'd run for a MTB XC race. They each have their strong points and drawbacks, but they're all useable for NM 'cross races.

For shoes, again use a pair of shoes suitable for MTB XC racing. So, whatever fits your foot well, accepts the proper cleats for the pedals you choose, and ideally has both some decent tread on the sole for running, as well as a couple holes up on the toe to mount spikes for the few courses where those are useful.

Some people prefer a slightly more flex sole, others like the stiffest carbon sole they can get, everyone likes a lighter shoe for running. Note that due to the absense of mud and real hills on the NM cx courses, our races are perhaps less running-centric than some.

I use the eggbeaters (at least I did when I raced CX- now I drink beer, and that's about it) and a carbon sole shoe. Easy entry on the eggbeaters- almost brainless in fact, which comes in handy when you have that bloody froth emitting from your lungs- and nice and light shoe which seems to take the abuse of the rocky runs quite well. Also, the float in those pedals is nice when you've taken a corner a bit fast and you end up sideways in the air- keeps your foot from taking the brunt of the impact and spreads it across your entire side!!! Have a great season- see y'all out there this year! OUCH... it hurts so good.

I like the Time ATAC and the egg beaters. Most people, that I know, use the egg beaters. If you need need a spare bike, someone will probably have one available with egg beaters. I don't like egg beaters with the platforms. I believe they are harder to click in to. Personally, I have never been in a situation where having the platform was necessary or useful.

Brad,
The eggbeaters with the platforms are called Candys. I suggest using them, so when you accidentally yell, "oh Candy", in your dreams, you can claim you were having dreams about your pedals. We are all big enough bike nerds, that's nearly a believable story.