I think the shiplap and tile sound good but no need for a mantle

You would need to remove some of it to see how it looks without it. Could be that there is a sizeable gap between the brick and the wood floor. Since that trim ties right in with all the other baseboard trim, it would look odd to change it to something different. Here's a good article I found regarding how hardwood floors should be installed around a brick fireplace: https://macwoods.com/hardwood-meets-brick-fireplace/ I find it concerning that there is no hearth beneath the fireplace. It is required that there be a non-combustible hearth at least 16" - 20" deep and 8" to 12" wider than the opening, depending on this size of the opening. You may want to consider adding Glass Doors to your fireplace if you plan on using it.

That is really not a built- in....it is a closet..and i would use it that way....add a door and make the shelves shallower toward the back....so everything easier to get at...while leaving some space in the front for taller things...like a broom or a dust mop...or to hang things on the sidewalls...since the wall space is not equal on each side...there is no pressure for both sides to match...leaving that sunny corner for some pretty plants or a very cool arched lamp that will swivel out to a small but comfy chair in front of the window...for reading or just watching the fun everyone is having in this family room...i also agree that shiplap is ideal for that wall (and could even incorporate a hidden door for the closet if desired) ...giving the room a little more relaxed feel for the more casual use that is intended..to me shiplap is timeless..(while enjoying more popularity in the moment)...it will always look good

First, that is likely a STONE veneer on the wall. If you don't like it you have to remove it. Or you could paint it. You can also remove part of the stone and add a timber mantel to the FP Here are the steps to get the stone off and the surround installed.