For most homes, you'll want a quality exterior latex paint.
What kind of paint do you use on eaves?
Exterior walls, eaves and fascia (the part the gutter sits on) are best painted in exterior acrylics which are water-based.
What color should I paint underside of eaves?
In general, ceilings under the eaves should be painted the same color as the siding, while the entire cornice (the trim that faces outward) should match the trim color. To make gutters and downspouts as inconspicuous as possible, paint them to blend in with the adjacent siding or trim.