You will need patch 1.74 for basic Civ 4, but that will be installed when you load BTS, however patching to 1.61 helps the install of BTS. I don't know if you have Warlords as well, I've left the instructions in for that, ignore them if you don't.
Try to follow this order when doing stuff:
install the most recent version of DirectX 9c from
Microsoft
Patch your Civ 4 to 1.61 (download it fresh from
here)
Install Warlords, immediately patch it to 2.08 (download it fresh from
here)
Install Beyond the Sword, immediately patch to 3.17 (download it fresh from
here).
then patch BTS to 3.19 (download it fresh from
here).
Important: As you run Win 7 make sure to run every installer and patch with admin rights, ie: right click on it and choose run as admin.