I would look at Satin or Eggshell. Satin is lower sheen than eggshell and one step up form flay which does not have much cleanability at is a more chalk like finish and will come off when rubbed to remove marks.

No semi gloss. Semi and satin belong on trim and doors and/or on exteriors.

You want matte on walls. Depends on the brand as far as what they call it. Modern, top tier matte finishes are wipeable.

SW Cashmere in matte or BenM's Aura in matte is the gloss level you're looking for, as examples.

I only use matte on the walls and satin for the trim.

Lori, she's asking about trim and doors.

I'd use the semi on those doors, baseboards, and other trim work. (I use gloss on mine)

As for the shiplap, You may want to go with a satin. I would never use matte or eggshell on any woodwork.

Matte or at the most Eggshell on the walls. Semi Gloss and Satin on the trim and doors.

We painted all our shiplap in matte paint, I don't like shiny wood. It looks more authentic to me without the shine.