I tend to like high gloss enamel paint on doors. They wipe clean better. Our doors in the condo are all done in Super White PM-1 by Benajamin Moore.

I would use a semi-gloss for the trim and if you want more drama, a gloss for the doors. Matte, which is almost flat, will not look finished or hold up well. Wood painted a flat finish looks like a primer, not a finished coat, to me. Use matte for your walls, flat for the ceiling, and give the trim and doors a nice shine.