For the trim, I would use an enamel, and usually trim, is done in either satin, or semi gloss, and if you really want it shiny, some do use a very glossy paint. I prefer semi gloss on mine, and since you used satin paint on the walls, I would probably use semi gloss on yours. As for the doors. Your beams, look a very dark brown, close to black. Therefore, so the doors match the trim, I would choose black fox, since it has a dark brown look to it. In the same sheen as you choose for the trim.

Paint finishes on doors and trim varies and is a personal choice. I always use satin for doors / trim and matte for walls / ceilings. Most paints now, reguardless of the the finish, are hardy and washable. Satin and matte hide most flaws in doors, trim and walls. Semi gloss and gloss show flaws. I even painted my front door with satin several years ago and it looks like it was just painted. I painted my whole home interior and front door with Behrs Ultra Paint and Primer in One. It goes on smoothly, no dripping, no issues, great quality. Best of luck on your journey!

Walls should be painted in a matte or eggshell finish, not satin. Satin or semi-gloss is for woodwork.

Manufacturers have conflicting names from one to another. Test out finishes in your home if not sure.

Thank you everyone! Yes I am leaning toward SW black fox for the doors, to match the beams. Will go with semi gloss for the trim and doors. It’s so true that finishes differ with manufacturer very widely. Am very happy with satin on the walls.