I think removing all loose stuff, dirt/grease and the key you make with sand paper are the most important things whatever the surface. I use pretty fine grade wet and dry with water even on furniture because I have it hanging around for car stuff, it lasts longer and leaves less grit and scratches than cheapo sandpaper. Let the surface dry thoroughly before you paint it if you're not using a water based paint.
I use something similar to this for all sorts of things from car body panels to furniture and it'll take all sorts of different paint. It'll give you a very good finish but you'll need a compressor to use it.
Very cheap on ebay these days too
A fine roller is good too or even a sponge. I even use a brush on occasion
It really depends on the effect you want.
Wood can be painted with a lot of different types of paint. Acrylic paint is probably good if you need to wash it or you want it water proof and don't want to use horrid gloss. I like to use a primer because they generally make for a tougher finish that is less prone to damage or peeling and they help give a more uniform finish using less paint if you use the right colour.