I would put a couple of rags underneath, to catch the spills, and have a small ice cream container to pour the rest in. Will be 1/4 - 1/2 cup or so.
When you put are putting the new filter on, fill it up near the top, so you don't have to prime as long afterwards. It takes a while to fill the whole space using the manual pump.
There are lots of posts on priming, but if the manual pump doesn't feel like its doing anything, you usually can turn the crank by hand, 1/2 turn or 1 turn and then retry - as the pump only works with the crank / camshaft on a certain stroke.