To change your painted brick color you have two choices, repaint or remove the old paint with a paint stripper. Adding another layer of paint will hide some of the characteristics of the brick. In order to use a masonry stain all of the original paint will have to be removed with a paint stripper.
Repainting is the easiest way to change the color of your brick since it is already painted. Painting brick is easy. Just follow these instructions, <a href="https://www.house-painting-info.com/painting-interior-brick.html">How to Paint Interior Brick</a>.
Stripping the paint from your brick is an option but is very difficult to do. Brick is very porous, so the primer and paint that is on it has soaked into the brick. It's nearly impossible to remove it all. It is very important that you protect all surfaces around the brick from damage from the paint stripper!
For any unpainted brick using a masonry stain is an excellent option. Masonry stain is available either as a semi-transparent or solid color depending on the effect you are after. The stain will keep the "characteristics" of the brick in tacked without producing a "caked up" finish. The solid color stain is like a thin paint, so it will have a similar look as paint.
The color you choose depends on your decor and the final out come you want. With paint and solid color stain any color can be used. Brick acts as a focal point no matter what color it is, using a contrasting accent color could help tie the room together. The color doesn't need to be dramatic; it can be a shade or two lighter or darker than your main color.
If you decide to paint use a good interior acrylic paint with a low sheen, eggshell or satin. The acrylic paint is easy to work with and the lower sheen will look better than a semi-gloss. Brick with a semi-gloss sheen will have the look of plastic. I do recommend a little sheen to help with dusting; flat paints hold onto the dust a little more than paint with a little sheen.