I think we had a similar question before, and if I remember correctly, most of us were in favour of Kodak Tri-X (real black and white film) and some in favour of KOdak T400 CN (chromogenic film for C-41 process, can be developed in colour chemistry).(posted 8717 days ago)For a first go with b/w I would recommend Kodak T400CN, as this film can be processed in any lab. Filmspeed is 400 ASA.
If you want true b/w prints you may have to find a lab willing to print on b/w paper. Some labs try to print it on colour paper, which might give it a colour cast.