RE: Recurve must have's for performance?
If the string hasn't been replaced in a while, I'd start with that. Dacron only (B-50 or B-500), endless or flemish will work fine, 12-14 strands, depending on the draw weight (15-16 if it's 60+lbs). Strike plate and rug rest also. If the shelf isn't crowned and radiused, put a piece of matchstick, toothpick, etc. under the strike plate and rug rest so the arrow has minimal contact.
String silencers if you plan to hunt with it, no need if you don't. A glove or tab will be good, to keep your fingers from getting sore. Make sure to get a good fit with either of these--if you get a glove, get one that is so tight you can barely get it on when it's new--when it breaks in it will be just right. A loose fitting glove can be more aggravating than a mother-in-law.
Do your homework on arrows--get the proper spine. Work on form before you worry about accuracy. Start out close--real close. Most of all, have fun!
Chad