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use a latex primer- I like Zinnzer 123- HomeDepot has it. Let it dry and sand with 300 or 400 grit. Then use a latex enamel for a gloss finish, or eggshell or flat depending on the finish you want.
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You asked how to paint and what kind of paint to use. So I told you.
Now you ask about polyurethane, so I will tell you about that too. For a poly finish , prime with lacquer sealer. Get the real deal not substitutes that call themselves lacquer. The fake ones work but have nasty stinky chemicals that make you sick if you breathe them. Real lacquer will not make you sick, but it is highly flammable for the first few minutes before it dries.
General C&ontractor
35 years of troubleshooting construction, remodel, component & material failures. What to do next