Painting brick is not cool. You can 'stain' the brick, but why? dyebrick.com is a great website. You can lighten the brick by not doing the paint or german schmear, which inhibits the ability for the brick to breathe and creates mold problems, but by doing this technique called romabio.com/limewash.  You can choose from whites, creams, beiges and gray, and it is fairly easy. I have read that a medium size home can be done for 30 dollars. Yours would certainly be a candidate, and I would than paint the siding a gray color that is very close to the shade of the limewash you use, so that the whole house appears more cohesive and attached. *** If, you should have a 2nd thought about dealing with the brick, just painting your home the color gray, that you have already in your brick, where the siding is, and than possibly doing the fascia boards in a slightly darker gray than the siding and the tone in the brick you have currently, would make your home look richer and elegant? Do the shutters in the slightly darker gray tone also, than your brick is. With the medium gray tone on your siding, and eaves that is in your brick, & the darker gray tone on your fascia, porch posts, and shutters, your brick will look so different, I don't think that limewashing it will need to be done. It is in such wonderful condition and such good quality, it just needs a bit darker siding, trim and than fascia and shutters and porch posts, to be very very pretty!! With your current windows, it will bring the home together as one unit and make the home appear larger and more grand. Such a pretty place you have! When you choose your gray color from your brick color, be certain to not veer into the green gray tones OR the blue gray tones. You want the gray that the brick is showing you, for the siding, and that same tone, only a shade more darker, for your shutters, fascia board, and porch posts. From what I see, I see a gray that is somewhat of an ashen color, silver almost, a black with lots of white in it?? ........ I would say on the computer screen that Glidden Brand PPG1012-4, Gray Frost , Steeple Gray PPG1012-5, and Volcanic Ash PPG1012-6, would be in the best realm for you. Either the first and 2nd color, or if when the sun shines the first is tooo light, than the 2nd color and the 3rd tone for the fascia, shutters, and porch posts. https://www.glidden.com/colors/grey-charcoal I would look at those and see if that is accurate on a sunny day in your area...I know too light of a hue will not have any color to the eye, and in the sun, you will know for sure. You don't want to create a very dark home, and light is what you have now, and you want it to look more rich in color value without being dark. Leaving your doors white will look very nice and clean.

I am not a fan of painting brick, especially when it is nice one like yours. Does your siding need to be painted?