Sounds like a fascia, if it runs along the bottom edge of the roof where the gutters would attach (if you lived in an area where it actually rained

)
Exterior semi-gloss is fine but if you have problems with peeling paint or blistering, you will need to scrape that off, sand a bit and check to see if it's a redwood, cedar or what type of wood. Redwood and cedar need a bit of special prep and a proper oil base primer to keep bleeding, staining, peeling and blistering to a minimum.
Then after the prep, exterior semi-gloss latex should be fine.