I rent and have permission to paint kitchen cupboards.
Janice: maybe this will help
Get a small roller lightly sand them sown with your hand then paint
I'd recommend using a good bonding primer like this one, after you clean the cabinets. Then you can paint with 2 coats of satin latex paint. Painting cabinets is a bit of work... if you've never painted before, you maybe should get a little experience with a dresser or something. There is a technique to painting so that the brush doesn't create drips as you go around the edge. Good to get a little know-how under your belt before you start that large of a commitment.
Here is how we painted ours: https://thehoneycombhome.com/?s=painted+cabinets