My experience is that if you buy 'bike grease' in a bike shop it will cost a fortune and last not very long. Apart from a couple of frivolous lbs grease purchases, I've always used one of those big tubs (Castrol/Halfords/whatever) of car grease. Usually lasts about 5 years*, costs about a fiver and is more than capable of standing up to the wear and tear that push bikes can dish out.
Generally goes on bearings (although lots of things are sealed these days), certain threads, metal on metal surfaces such as crank/bb, stem/steer, seatpost/frame, inner/outer cable, etc. Used to be great for elastomer forks and v-brake bosses too but no need these days.