Choosing the right color to stain brick will be tough. Remember, you're adding that color to what is already thaere. Stain some test bricks to determine the outcome. You can paint brick with a latex (alkyd) paint. It's breathable. A stain is a very thin paint. Meaning more solvent and less solids. To paint brick you want to use a thin paint - think cheaper contractor grade or you'll need to add water. Make sure it's an exterior grade. You'll need to clean the surface to remove all dirt and mildew. Issues with the brick, air expcaping or moisture problems will only be amplified once you paint over the brick. Think of repainting over peeling over wood. The problem will just return. My advice would be to spray it and then back brush it. I'd have a reputable contractor recommended by a SW store do the cleaning and painting. It'll be worth it. SW has a help line you can call or you can ask in a sote or they can call the helpline for you. The guys on that help line have forgotten more about coatings than most of us will every know. Also, don't listen to anyone in Home Depot or Lowe's. They don't know anything about paint.