If you have a hard drive over 8 GB in size, you must partition it. The partition containing OS X must be within the first 8 GB of space or you will not be able to run OS X. (If you are creating the partion within OS X, it must be 7.45 GB or smaller as reported by Disk Utility, because sometimes a GB is billion bytes and sometimes it's 1,073,741,824 bytes.)
You can only boot OS X from a "master" drive in the beige G3. This applies to hard drives and CD-ROM drives. If the CD-ROM is set to slave, you will not be able to install OS X. If the hard drive is set to slave, you will not be able to boot from it.
Non-Apple upgrades and peripherals (such as unsupported USB devices, replacement drives, and third-party memory) may cause problems when installing or booting into Mac OS X.
Be sure to read and follow Apple's "Read Before You Install" instructions to increase the likelihood of getting OS X installed and running on the first try.
The beige G3 is not officially supported under OS X 10.3 (Panther), but it does work with 10.2.8 and earlier. Panther can be installed using XPostFacto 3, although built-in video is not currently supported.