How would I go about painting exterior brick?
This is a tough one that will take a bit of work. From personal experience, any time you're going to be applying paint/primer/etc. to any kind of questionable masonry and mixed surfaces, it's going to be a good idea to clean/prep in several stages, then apply a masonry grade primer.

Depending on if there was any kind of debris, mildew, moss growing on the surface, a brush and/or pressure washer could be suggested. If the surfaces are clean and evenly covered, I would use a good stiff deck brush or similar.

I would also suggest a chemical cleaner/stripper containing muriatic acid, which will have a mild etching effect and ensure good adhesion with whatever you decide to paint with.

Then proceed with a good masonry primer, following manufacturers specifications. The same would apply for your paint.

In most of my jobs and personal projects, I would say a good paint job is 90% preparation, 9% good product and 1% skill.

In short, treat all surfaces the same, clean and prep evenly and somewhat indiscriminately. I would suggest a standard latex acrylic. Elastomeric paints tends to be heavier and really suited to new construction and initial application. If the house is older, it's most likely done most of its settling. 

This reference is in regards to commercial new construction, but a lot of the premise will be the same.
http://www.masonrymagazine.com/5-08/cleaning.html

Good luck with the project.