Acrylic paint should work. I use Folk Art or Apple Barrel. The wood does not need to be sanded but it would not hurt if you did sand. Since wood is porous you may want to use a primer or acrylic white paint as a base. If you are going to decorate the egg but you want the wood finish to be visible under a design; use a matt or gloss as the primer.
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BC 11/23/2008
Low porosity, Fine/Medium Texture, S-Curls

Co-wash: VO5 Tea Therapy
Rinse Out: Garnier Sleek 'n Shine (subject to change)
Styler: Long Aid Curl Activator

Dislikes: Proteins (except occasional Silk protein), Cones, Oils