preparation is key. cleaning/sanding/priming are a must. Use a paint meant for wood trim, not drywall. BM Advance or SW ProClassic are two of the best. Plenty of how to videos and such all over. You can check Pinterest for links to blogs w/step by step.

Hi, I'm also in the process of painting a bathroom vanity from a very dark stained wood to white. If you have a deep grain or any type of veneer, I highly recommend priming first with a Bondable latex primer and a dense foam roller for paint adhesion, blocking dark staining, and a smooth finish. Good luck!

Use a deglosser first.

Zinsser oil base primer is one of the better one. you still have to sand. de-glossing only does so much. I don't know what shape your current cabinets are in, but I like to sand things smooth. use a glossy paint will show every defect. If you have dings and dents, use a wood filler after you strip off the old finish. sand and smooth, prime, do a fine sanding again, wipe clean, now you can paint.