I am painting the entire living room and the brick.

I would remove the baseboard along the bottom of the fireplace & replace it with a piece of quarter round. It looks odd in its current state.

I would not paint the brick. You can stain brick or lime wash it, but paint will be a big mess if you ever build a fire.

I used Zinsser Bulls Eye primer (water-based), two coats as I recall, then two coats of a Valspar white semi-gloss. It was one of the off-the-shelf whites. Got sick of trying to pick the right white from all the chips since none looked right. Painted it last fall & used the fireplace a lot last winter. Looked a lot better with our new furniture, so after hesitating some, we're glad with our decision to paint.

Just search YouTube for videos for various ways to address the brick. You can paint, but you can also use concrete stain, (no priming required) and it soaks into the brick instead of just being applied on top.

If you want more depth to the brick you can use BrickANew

https://youtu.be/FarofFXZcvI

Also consider German Mortar Smear which is another technique for the brick.