1. Ease the corners and edges with a file or corner rounder (or router) before you do anything. Sharp edges will not allow enough surface area for a proper film of paint to form. The sharp edge corners will fail first. Lightly sand and throughly clean all surfaces with a tack cloth.
2. Before you fill the voids with wood putty (wood plastic), prime the cut edges. The raw wood will draw moisture from the un-set wood putty, making it crumbly when dry (in addition, the presence of calcium carbonate in wood putty is another reason not to use it on raw wood in order to prevent degradation). The primer will help prevent that from happening. Do not use "wood filler" to fill the voids (there is a difference between wood putty and the various types of wood filler).
3. Two to three additional coats of alkyd based (not fast drying) primer on the cut edges (after the putty has dried, sanding in between coats). At least one additional coat of primer on the flat surfaces on pre-primed boards, two to three coats on raw MDO.
4. Top coat with the finish of your choice. Assuming you are doing this by hand and not spraying acrylic polyurethane (best choice) use a good quality acrylic latex or alkyd enamel. Bulletin enamel works great for a really smooth, glassy surface, but latex will likely last longer on an outdoor sign.