Another vote for Tri-X. A great film for beginners, and still a personal favorite for plenty of uses after 35+ years experience. Develop in D-76 1:1 for dependably excellent results.(posted 8688 days ago)If you're going to be in mega-bright light or require prints larger than 8x10, Plus-X (which is slower and finer-grained than Tri-X) is another good choice.
If you're in an English sphere of influence and they're notably cheaper, the Ilford equivalents, HP5 Plus (125) and FP4 Plus (400), are pretty similar. If you're in Europe, Agfapan APX 400 and 100 are also similar (and the 100-speed in particular is a very beautiful film).
Just stay away from those newfangled Kodak T-Max films and Ilford Delta films - they're wonderful in their way, but a bit tricky for beginners. When you have your darkroom technique down solidly, be sure to give them a try... In some ways, this is the golden age of b/w film - there's quite a selction, and they're basically ALL excellent!