Take you old bottom bracket to a local bicycle shop and ask for a cartridge replacement. They should (hopefully, will) ensure that you get the right thread size and spindle length. You might need a special tool to install the bottom bracket, if it is the modern cartridge one. If that is the case, buy the tool, ask to borrow the tool, or get the shop to install the bottom bracket. They should not charge much, since the old one is already removed.