I ride a couple DIY centuries a year, although not on my fixed gear. However, a friend always joins us for our Chicago to Milwaukee century and he rides it fixed.
Eat: Clif bars, Mojo bars, Stinger Waffles, trail mix, bananas, Jelly Belly sports beans for electrolytes. Personally, I HATE gels and refuse to eat them. The chews are ok but that gel stuff is nasty. I do sometimes get something like beef jerky just because you get SO SICK of everything being sweet and carby. Or you can stop for a cheeseburger for lunch.
Drink: Water and watered-down Gatorade. You can buy single-serve packets of Gatorade power that make it easy to mix up Gatorade throughout the day. Those nuun tablets are ok too. I have two bottle cages and one bottle is always plain water and one is always half-strength Gatorade/nuun. If this is not a charity ride where they are giving you water, a good idea is to stop at gas stations/convenience stores and split a gallon jug of water with your friends. Much cheaper than each buying individual bottles.
Wear: Shorts with chamois, for sure. Chamois cream is a good idea. Jersey so you can have easy access to sunglasses, chapstick, sunscreen, one of your foods, a handkerchief... October in MO, maybe you'll want arm warmers or a long sleeve shirt.
Ride: Steady pace, don't start out pushing it. Take frequent breaks if the group does.
Bring: Tools and tubes if there are no SAG cars arranged.
It might be a good idea to try to get one or two 65-70 mile rides in before your century. If nothing else, make sure your bike fits as well as possible. Fit issues really make themselves known on a century.
Good luck! You'll see - it's really fun and not all that hard.