First of all make sure you have the OS 9 drivers installed on the drive. You can tell this from System Profiler in Tiger. If they're not installed, you can't boot from OS 9-the only real way to fix that is to reformat the drive while installing drivers. Otherwise, if you do a drag and drop install, you can get "stuck" trying to boot into OS 9 when OS 9 can't actually see the HDD.
Assuming that they are there, I'd suggest burning a an OS 9.2.1 install disk then booting off that and running the installer. Drag and drop can work, and I've used it in specific situations(such as when copying special OS 9 builds for late computers or when I just need a system folder for Classic) but IMO I find running the installer is the overall best option. If nothing else, it will ensure that all the extensions your computer needs to function correctly are working(there may be features that don't work if you drag and drop from a different computer).
Booting from an install disk also gives you a chance to double check for OS 9 drivers. If you boot from the install disk and don't see the HDD on the desktop, you will know that the drivers aren't installed(you may also be bugged to initialize the HDD-don't do it!).
OS X doesn't have any problems co-existing along side OS 9. This was the standard way the factory installed "back in the day" and is how it will be done if you run restore disks that install both 9 and X.
