Paint it white or a white wash?

It's unanimous! White always looks good in sunroom or porch.

Here is one example with exposed brick wall.

white

I really like the texture it provides to the room. What type of paint should be used on the brick?

What kind of paint should be used on the brick?

Just white wash it.

I think white wash would be more charming if the brick tone were different. Here, I like a full application of white paint as the best solution. You will have more charm and texture, but it won't set your color palette.

All the paint companies have a masonry formulation that breathes differently - don't buy the elastomeric option, that is for outdoors. Sherwin Williams has some good warm whites - i like steamed milk for this application. http://www.sherwin-williams.com/homeowners/color/find-and-explore-colors/paint-colors-by-collection/whites-and-lights/warmer-whites/
http://www.sherwin-williams.com/homeowners/color/find-and-explore-colors/paint-colors-by-family/SW7554/