forget bmx - they have different mount for the saddle.
generally road and mountain bike are the same, the latter tend to be longer and larger diameter.
your first step is to figure out the internal diameter of your seat tube - if your post isfitted without a shim, then the posts are usually marked with the diameter.
next you need to figure the length of post - these start from around 200 mm up to 400 mm (you can get shorter and longer but that would imply your frame is not the right size).
then how much you want to spend? cheap and cheerful are kalloy; you can get rade face, thomson, easton etc. in alloy and carbon fibre.