I wouldn't do anything to the brick. Once you paint or stain it, it becomes a maintenance item AND doesn't totally get removed should it ever be cleaned.
I, as you, suggest that you have it 'covered' with wood and moldings. IMO, painting it MAY devaluate the price a little. If you plan on staying there until you're old and grey, paint it. If not, do something that's 'reversible'.