What kind of paint for my new doors, baseboards, etc...?

We recently had new doors, door casings, window molding and casings, baseboards and a mantel installed. Its MDF paint grade, what kind of paint should we use? Should we use a roller or a brush? What kind? We painted a section around a door with semi gloss white paint and it came out streaked and sloppy, so I'm trying to get some advise on what we can do differently. Anything will help as I'm tired of it looking very dull and unfinished. Thanks!!