Seal crack between brick wall and drywall
You don't fill in the gap between drywall in brick.  Caulk, mud, plaster, whatever will not keep this area from having problems.  I have done tons of drywall to brick and there is simply a small gap there.  Anything else doesn't look right.  

I have also seen small t-molding placed there and it looks... OK but not right.  

I have seen caulk and it just looks bad because the brick isn't a flat edge against the drywall.  It has valleys for mortar and these take a lot of extra caulk.

Then you can plaster over the entire brick or backer board to get rid of gap but you are losing the brick.  

I have brick fireplace right next to custom shelving in my house and really glad I didn't caulk it.  The key for your situation is a nice straight thin drywall line.