Most laminate or Formica countertops can be painted easily, if you want to give them a fresh, new look. The procedure for painting countertops is similar: clean and sand, prime and paint. The primer must grip the counter surface like superglue, and the paint needs to dry to a tough finish that can withstand scrubbing, cleaners and a lot of abuse. When it comes to choosing the best kind of paint to use, you have several options.
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Once the countertop is sanded, cleaned and ready to paint, you need to choose a paint system. Do not rely on a hardware or "big box" home store for guidance or the best products. Go to a dedicated paint store, where professional painters get their paint. These shops have a much wider selection of specialty paints and primers, and extremely knowledgeable staff. Do not use budget paint for this project. With paint, the old adage "you get what you pay for" is almost always true.
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Primer
Use an oil-based primer if you are going to use oil-based enamel for a finish coat. There are some water-based acrylic primers that claim to work well for tough-to-paint surfaces like counter tops, but they will not rival an oil primer for adhesion, and without great adhesion, you are wasting your time because the paint will start chipping off within months.
Paint
Once you have primed the countertops, you can use a satin or semi-gloss oil-based enamel. Most are perfectly safe for food preparation, but make sure the paint store knows what that you are planning to use the paint on your countertop. For extra protection, use a urethane modified clear finish over the oil enamel. Buy a clear finish formulated for flooring, as this is extremely tough and durable.
There are two kinds of paint that require no priming, but are more difficult to use. Two-part epoxy or appliance paint is typically applied with a sprayer, but some formulas can be painted with a foam roller and brush. If the countertop is not very large, there are some spray epoxy paints that can work well. Some are available in both solid colors and a flecked or pebbled granite finish. A benefit of spray finishes is that if the finish gets chipped or marred, it is very easy to touch up.
Your other option is the melamine finish. This require no primer, but takes three or four coats, and once done, the countertop cannot be used for several days until cured.
No paint, with the possible exception of a professionally-applied epoxy system, is going to be quite as durable as the original countertop. Invest in a large cutting board and avoid putting very hot pans directly on the countertop.