After sanding, wipe down with a damp cloth (use white spirit to dampen cloth) and allow to dry.
If there are any knots in the wood (pine is usually very 'knotty'), you will need to treat these at this stage with knotting compound, to avoid brown stains appearing through the final finish. There are 2 types, try to get the clear type.
Personally, I would use a primer coat first then 1 or maybe 2 coats of undercoat before your top coat. To make life a little easier, I always use acrylic primer/undercoat. This is a water based all-in-one product and dries a lot quicker than oil based primer and undercoats, it also makes cleaning up a lot easier. 2 or 3 coats should provide a solid base for your top coat.
Ideally you should sand and wipe down the woodwork (as above) after each coat has dried. If you don't, at least make sure that you do it before your topcoat..
As far as your topcoat goes, I concur with clever trev that satinwood is a much 'classier' finish, (or eggshell as it is more traditionally known. Generally, eggshell is oil-based and satinwood is water based. I think a few years ago one of the big paint companies decided to rebrand the little used eggshell paint as satinwood...but I digress.)
I have found that the water based version may need 2 coats to provide the depth of finish that the oil-based variety offers...