I always prime and paint after routing except when I "V" carve inwards. Here is my procedure:
1) Rout job
2) Wash with water/garden hose and let dry
3) Brush prime
4) 2 coats of primer sprayed
5) 2 coats finish
If it's a sign that is placed distantly, I will not prime, just use finish coat. I use nothing but quality exterior grade latex satin paint. I paint all my raised copy with a 3" foam roller.
If the sign has any "v" carvings inward, I will practically finish the sign, cover carving area with paint mask, then re-align sign onto the router and carve through the paint mask into the foam. Apply primer and finish coat into carving and remove paint mask.
As for router bits, I use Gerber V carve bits. I mostly use 60, 90, 120 & 150 degree bits. I know they have a few more sizes, check there website for complete listings.
Good Luck!