I don't drink at all but I serve a lot of rum at my tiki bar. My guests have a few favorites.
Ron Zacapa Centenario Solera Grande Reserve - probably the favorite sipping rum. Not cheap, but worth it.
For mixing - Plantation 5 year Olde Grande Reserve Barbados Rum, don't let the low price fool you if you can find it. Very good and very inexpensive
Demerara Rum - Demerara Distillers El Dorade "12 year" Guayana Rum, go for Lemon Hart 151 Demerara if you want to go old school (the original zombie) and can handle the kick. Both are fairly reasonably priced.
You CAN buy cheap rum, but don't. A good bottle of rum goes just as far or farther because folks actually drink less of it because of the better flavor. A good rum will hold up well in a mixed drink, even just an ounce at a time.
dcman2