The list on this page isn’t complete (i.e., I’ll note some other ingredients in specific recipes)
http://www.drinkboy.com has a bunch of recipes that you might want to peruse.
A few days ahead of time, have your folks get some frozen cherries, dump them in a jar, fill the jar with drinkable brandy, and stick it in the fridge till the day of the party. Use those as maraschino cherries.
Bitters: You need them. I’d recommend picking up some Fee Bros. Angostura bitters (just get the regular stuff, not the aged bitters) and some orange bitters (Regan’s is preferable, otherwise Fee Bros.) Angostura brand angostura bitters are also good.
Whiskey: I prefer rye to bourbon, though there are some drinks that call for the latter. I’d recommend the Rittenhouse bonded (100-proof) rye—it’s both quite cheap and quite good. If all you can find is Old Overholt, that’s acceptable. Don’t use Wild Turkey.
Gin: Plymouth is what you want. Second choice is Miller’s.
Vermouth: Get fresh bottles of both sweet and dry vermouth—even though it’s fortified, it’s still wine and it does go bad over time. Keep it in the fridge. If you feel like ordering stuff over the Internet, I highly recommend Carpano Antica sweet vermouth. Vya also makes sweet and dry vermouth that are pretty good. Otherwise, just use whatever you can find.
Brandy: I’m not particularly familiar with brandy. I just use the cheap stuff from Remy Martin.
Apple brandy: Yes, you should classify this separately from grape brandy. If you feel like ordering stuff over the Internet, I highly recommend Laird’s bonded (100-proof) applejack—I think they label it “Straight Apple Brandy”. The regular applejack will do in a pinch, but it’s not that great. Laird’s also has a couple of types of aged apple brandy which is pretty good, and then there’s “calvados”—French apple brandy. This can be good, but can be pricey. There’s also some other domestic apple brandy.
Triple sec: Just go with Cointreau. It’s expensive but worth it.
Rum: For white rum, Cruzan is my go-to brand. Mount Gay Special Reserve is also good, but has a more pronounced flavor with vegetal notes. For dark rum, everybody seems to have their own preferences. If you feel like spending a lot of money, I like Ron Zacapa or Zaya; Mount Gay Barbados Sugar Cane Rum is cheaper but also quite good. The other dark rums from Mount Gay are fine for mixing.
Sugar: Get sugar cubes. Regular white ones are okay, but you might want to go to some place like Whole Foods and get something like demerara sugar cubes (look for cubes that look like they’re made out of brown sugar). While you’re there, you might also want to pick up some light agave nectar (I use Madhava brand).
You’ll also want fresh lemons, limes, and oranges.
Always, always, always measure your ingredients. Oxo makes little 2-oz measuring cups that are great for this.