Bicycle Tutor

I am trying to build my road bike with Tiagra gears and want to ask how to choose a BB. There are so many BB different brands, different models. how to choose a right one.

Depends on the frame. The BB has to match the frame. Also, the crank set should work well with a Tiagra setup. I'd approach this problem like that (assuming you have a modern road bike):
- find out, which crank sets work with Tiagra (why not go with a Tiagra crankset?)
- look at the requirements of the crank set: connection (octalink, tapered square, whatever) and axle width and choose a BB that fits these (and, of course, the frame).
If you have an older road bike then you might have to stick to whatever BB you can find that fits your frame. It'll most probably have a tapered square axle which narrows down the selection of cranks.