what your calling "grease" is probably contaminated lubricant what i typically recommend to customers with gunky chains is to carefully clean the chain with a degreaser, making sure that none of it goes into your bottom bracket or hub in fact taking the wheel off is sometimes easier, and then lightly applying new lube to the chain. as far as choosing a lube goes typically a dry teflon lube will do but if your doing mountain biking then your probably going to need something cleaner and drier like a wax lube and if you constantly put alot of miles on your bike then i recomend a wet lube