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.

Im working on a bike with the same issues. Old bike with newer style BB. First decide on a crank. Avoid something new and exotic. Square taper will probably work best. Next,you need to know where the crank rings are going to run in relation to the seat tube. (distance) And also front derailleur to center of the two rings. The easiest way here would be to install old crank in BB shell , then take some measurements. FYI- BB's are measured by threaded section x spindle length. i.e. 68x113. 68mm being the threaded section width, (common), and 115 the spindle, or crankshaft length. Anyways, your FD has to be 'in range' of the two rings. For my old bike with a 6 speed rear freewheel, I ended up with a 68x107mm BB. It stands to reason that a 10 speed bike would probably run a longer spindle in order to align better with the rear cassette. There are some other #s on the BB also,1.37x24 (I think) these refer to the thread diameter and thread pitch.(common).