Hey, this one's really simple. You want to go randoing, you must have a rando club in the area. So show up at a brevet start and drool on bikes. Around here, the hard core stylists will have some sort custom steel or ti bike with French bar bag, polished metal fenders, dyno hub, custom light mounts, and all the rest of it. The fast boys will be on carbon, no hub, but may also have custom light mounts. Everyone else will be "run what ya brung." Every kind of thing. If you'd ride a century on it, you can rando on it. I ride an old carbon race bike, clip-on fenders if any and 23c tires. I find my comfort in completing the course as quickly as I reasonably can, sitting in a soft chair, eating, and then a shower and bed. Ummm.
I suppose the only really trick thing that makes a huge difference is a waterproof cue sheet holder:
http://www.rei.com/product/637973/bar-map-holder-small
or similar. It's really about staying on course and finishing in the time limit.