The main question is are you going to be processing it?
If so for b&w you have a vast choice, I generally use Ilford films, such as FP4+ (asa 125), HP5+(asa 400), and Delta 3200 (asa 3200), these are all classic b&w emulsions which are nice and easy to process, and excellent if you will be doing your processing. The Delta range use a different kind of emulsion which creates finer, smoother grain but are more fussy about exposure and processing.
If you're taking them to a shop to be processed then it's easier to stick with chromogenic film, which is B&W film that can be developed in C-41 (regular colour film) chemistry, the advantage being that they can pop it in the 1 hour photo machine and give you good results. Of this type I have found Ilford XP-2 Super (asa 400) to be the best, as it's very versatile (can be shot between asa 200 - 800) and gives excellent practically grainless results. Kodak, and Fuji also do chromogenic films.
I'd reccomend processing your own, as it's easy, fun, and cheap, but my film choices are above.
Hope that helps?
Col