Check out this page- <a href="https://www.house-painting-info.com/painting-doors.html">Painting Doors</a>. It describes all of the steps needed to paint your doors. Don't scrimp on the prep.
The paint you use can be any good interior acrylic wall/trim paint. The sheen can be satin, semi-gloss or gloss depending on your preferences. There are many good paints on the market that can easily meet your needs. I recommend visiting your local paint store. They will have several options to suit your budget.