Always run the most recent version of DirectX. If a game install asks you if you wish to install ANY VERSION AT ALL say NO!!!! Get DirectX from Windows update site and ONLY from there.
DirectX is backwards compatible for earlier versions and will run them.
If a game refuses to recognise DirectX as installed when there's a later version on the system, I'd suggest you throw the game away, as it's poorly coded ;)
ALWAYS choose 'Custom install' for games, so you can specify which directory you want the game installed to, which stupid online multiplayer components you wish to omit (for example because the game is old and no-one bloodywell PLAYS it online anymore) and so on.
DirectX is ONLY included on game CDs in case your system doesn't already have it installed ;)