Acrylic paints and watercolors are the best options for wood burning. As these paints are water-based, the colors sit well on the wooden surface. Besides, both these paints dry fast, taking about half an hour only. Acrylics have a thick consistency which makes them suitable for more versatile uses. On the other hand, oil-based paints don't stick to the wooden surface and take a long time to dry.  Remember, no matter which type of paint you choose, make sure it doesn't contain any additives or binders that might damage the wood.