Add 1 1/2 gallons of antifreeze, and fill the rest of the way with water for a 50/50 mix. The heater core won't usually cause an overheat problem, if it's bad you'll have no heat. I recommend buying a flush kit at any parts store. It has a fitting allowing you to hook up a waterhose and flush the cooling system properly.
Here's a website to help you drain, flush, fill and bleed your cooling system...
http://www.autozone.com/servlet/UiBr...d4.jsp#hd1-1-5