How do I finish the top of my makeup desk?

You are on the right track with sanding to remove everything that is on top. The key would be to progressively use a higher grit sandpaper and a finishing sand paper so you won't have any scratches. After you clean all dust off after sanding, use a good quality paint primer. That will help smooth out the final coat of paint and help it stick so it doesn't chip. The work is all in the preparation to make it look good.

Hello, I would consider sand and repaint. I would not personally chose appliance enamel as it is very unforgiving in the final finishes appearance.

Consider posting a photo to best explain your situation.

Use Milk Paint or any other textured paint to hide the blemishes. It is either that or using spackle in the places that the blemishes are as a Prep before another coat of paint.

I just redid my desktop, which was a worn laminate. I used Kraft paper. Sand the surface and wipe that down with some alcohol. Take the brown Kraft paper and cut it a bit larger than the surface. Wet the paper and let that sit a bit and paint a thick layer of Modge Podge onto the desk. While that's still wet, take the paper and layer it over the surface being careful there's no bubbles. Use a damp sponge and keep working the paper to remove any bubbles that are between the desk surface and the paper. If you can't seem to get them out, use a razor blade and nick the bubble and smooth the paper. Once that's done, paint the surface with 2 more layers of Modge Podge, drying between layers. Finally, put a layer of Polyurethane over the top. I used the water based version and the desk is perfect.

Milk paint or chalk paint would work well. This shows the milk paint I used on my kitchen cabinets: http://momhomeguide.com/my-painted-kitchen-cabinets-a-year-later/