Crank arm length is dependant on a couple of things. First and foremost it has to do with a rider's leg length. Shorter leg length = shorter crank arm length.

The other thing that determines crank arm length is type of riding. For example, DHers and Slalom racers sometimes use a shorter crank to have better pedal clearance without having to modify the frame geometry with a higher bottom bracket.

Also, a lot of BMX racers will choose a longer crank arm to have better torque and faster speeds coming out of the gate for the holeshot.

Again, a lot of single speeders use longer cranks for better torque on climbs.

Me, I've got a long torsoe and short legs. I could get by with a 170 mm crank, but a 175 "feels" best for the majority of riding I do.

Finally, bb size is more dependent on your frame, not the crank. You just have to have the proper interface (i.e. Ocatalink, ISIS, Square taper). Your frame will determine the size bb width and axle length. There are two numbers for a bb. The first is the bb shell width the second is the axle length. For e.g. a 68/112 has a bb shell width of 68 (72 is the other choice) and axle lengths can be anywhere from 108 to as wide as 132 (I think! - that's pretty honking wide!) A range from 112 to 120 is most common.

L8R