Yes you can paint brick and it hold paint very well, and you can get easily ten years out a paint job.

You will need to wash the brick to remove dirt amd mildew and that can be done with a prodcut called JOMAX. You don't need vinegar.

Go to a local paint store (not a big box) and tell them you are painting brick for the first time and they will give you the correct primer and topcoat system to do the job. It needs to be a masonry primer and not just regular exterior primer.