We don't use our fireplace and would like the wall space back. Is there a right way to seal everything up? My approach would be to cap the chimney top and plywood + drywall the front opening.
Removing the facade is not usually very hard. Where you will run into quite a bit of work for a brick fireplace is with the hearth. Usually these are poured and removal may require a jackhammer, sometimes only a heavy demo hammer is needed. As your hearth is above the floor level it may be part of the base of the chimney. So removal is not a minor job but could be done DIY.
I understand you want to reclaim the space but for me it would be all or nothing . Remove the entire thing for a few inches of space, or install a gas or pellet stove insert and seal it so you don’t loose heat up the stack. I have installed gas log inserts that ran for a month on a 5 gallon propane tank, this increases the home value verses the cost of demo and reducing the home value. I did remove a fireplace in my 1930 farm home as it was in a poor location and was not safe to use. However I added a free standing high efficiency stove in another room (addition). I would use caution with a partial demo as that could be considered a liability for future sales this is why I say all or nothing, a fireplace that is not usable will reduce the value or has in the past, a simple change to a gas log insert brought the value of one home we flipped ~15k and that was 20 years ago.