Welcome to the hobby!
After you get a lure carved out, line tie and hook hangers in place, and lip added, it's a great idea to test swim it before you paint it. Seal it with either super glue, poly, epoxy, or some other sort of waterproof sealer. This will also give you a smoother base to paint on.
As for paint, I think many paints work. It's the final top coat that holds it together, protecting both the paint and the lure in general. I started with spray paints, have used brushes on acrylic paint, airbrushed water based paints, and even used nail polish. Each medium has strengths and weaknesses.
Airbrushes are nice and provide the easiest medium for blending colors, fading colors, and adding fine detail.
Most people use epoxy for the top coat because of its strength and durability, as well as relative easy of use and accessibility. Other top coats work. Like paints, each option has strengths and weaknesses.