Are there ingredients I should avoid in a brine?
A brine serves two purposes: to make the meat moist and flavorful.

How the moist part works: "Brining makes cooked meat moister by hydrating the cells of its muscle tissue before cooking, via the process of osmosis, and by allowing the cells to hold on to the water while they are cooked, via the process of denaturation." (Wikipedia)

It makes the meat flavorful by acting the same way a marinade does. So you're pretty safe following "standard" marinating rules. Chief among those being that you want to avoid using too much acid or using acid for too long because it might make the meat mushy.

Avoid alcohol as well. "If your marinating anything with alcohol, cook the alcohol off first. Alcohol doesn't tenderize; cooking tenderizes. Alcohol in a marinade in effect cooks the exterior of the meat, preventing the meat from fully absorbing the flavors in the marinade." - Thomas Keller, the French Laundry Cookbook

Remember to use a nonreactive container (no metal) and avoid ingredients like olive oil that solidify when chilled.