Let's look at your options...
Brisket - the gold standard of BBQ beef. Becomes very tender when cooked low and slow. An inexpensive cut of meat (if you know the right places) Cons: Very small window between undercooked (to tenderness) and dried out. Only fat is in the fat cap, meaning that you lose lots of rendered drippings every time the meat is turned. Not very spit-friendly.
Rib Roast - Good marbling throughout. Not much connective tissue to break down in the meat. Cooks relatively quickly, even at lower temps. Delicious. Cons: If you have to cook to a more "done" temperature depending on your audience, the meat could become tough and dry.
Eye of Round - Cheap. Fits on a rotisserie stake perfectly. Cooks evenly throughout. Cons: even a good round roast has a more dry, tough texture.
Chuck - Tender and flavorful. Very forgiving. Excellent for low/slow cooking. Lots of marbling throughout the meat to keep it moist during cooking. Cons: Falls apart when cooked properly, meaning it would be difficult to keep it on a spit. Best served as pulled beef, which may not be what you're seeking.
Sirloin - Juicy, full of beefy flavor. Lean. Cons: it is easy to turn out a piece of sirloin that is like shoe leather.
Tenderloin - Tender, and tasty. Forgives cooking beyond medium if done properly. Cons: Very expensive.
Beef back ribs - Tender, good fat content. Good for slow cooking. Cons: can be difficult to serve/eat.
I don't really know what I'd pick here. I'd almost certainly eliminate brisket, eye of round, and sirloin, for various reasons, if I'm sticking to spit-cooking. I'd be on the fence with chuck -- you'd have to come up with some kind of cage-type mechanism to keep the chuck roast(s) together. So I'd lean toward rib roasts or tenderloins. Both are pricey, but they are worth it. Only problem is, if you have people who insist upon medium-well or greater meat, you'll have to figure out what to do. Maybe cook to medium and sear off chunks for the people who want theirs more cooked?
Another intriguing option might be beef back ribs. I saw an episode of Primal Grill with Steven Raichlen where he made giant beef ribs on an open fire, Argentinian style. He put the ribs on big stakes and pounded them into the ground next to the fire, turning them around every so often.
As far as wood goes, I'd suggest oak and/or hickory. Personally, I like those with beef. Perhaps the best strategy would be to build a fire with charcoal, just some regular briquettes (no Match Light!!!). Then continuously feed some wood logs to the fire during the cooking process. The smoke flavor you impart will not be as profound as it would be in a smoker, but that may be appropriate to your audience.
I'd suggest getting small cuts of each of the meats, put them all on the same spit, and give it a test in your backyard. Whatever you don't like, toss it into some stew or chili. Through trial and error, you can get your fire method right, and get some good meat in the process. Win-win!