I used to use Penrite water pump grease but they stopped making it. I now use an additive that goes in the water and is oily and does not make the hoses rot like most do.
The amount of grease needed is remarkably little. When I assemble a water pump, I prime the rear bearing with a grease gun and only leave a trace of grease in the bush when I assemble. After that, I use the screw on cover tot he grease nipple only. About a match head or two of grease and screw it on. The grease is forced into the bearing and it is unlikely that your cooling system will become clogged by grease. Even then, every now and then (say, 20,000 miles), I use a dishwasher detergent tablet to dissolve any grease that might have found its way in there, then add my bottler of Motor Medic water pump lube and I'm good for another long drive.
BTW, water pump grease is not grease at all. It is a wax that melts by the time the engine reaches operating temperature and remelts each time you drive.
