Someone was giving a way a rocking chair down the road, picked it up and took it home. Too weak to sit in but I painted it with some Rustoleum for metal baseboards, sand color, and put it in the front yard with flowers in it. Should last rtwo or three years.
A 2 step stool we picked up and painted with automotive paint. Using it for an indoor plant stand.

Point is, use whatever you have and want for a color. Clean as needed but don't make a big production out of it. For $1 you can enjoy it for a year, pitch it and buy something new.

You can use a water based primer. You can also just get a aerosol can of oil based Kilz or BIN and just shoot the spots with that. No need to get out a brush/roller in oil based.

You can use water-based primer. In fact, if the primer is already white, you may not need to put an additional coat of white paint over it. Semi-gloss paint is fairly shiny, and if you are going for a shabby-chic look, you wouldn't want it shiny. If you want just a cute, white table...you have everything you need!