The Beige has it's issueswith OS X, server or otherwise.
It's possible to install OS X onto a beige, but neither the Beige or the OS will like it.
Check and make sure your HD is EIDE (Mac OS Extended) formatted and of less than 15Gb before attempting the install. OS X does truly ugly things otherwise on either Beige machines or Blue and Whites. Also: on both those models, the ATA circuitry on the Mobo has a bit of a flakey streak and doesn't like larger or more than 1 drive.Install OS9 from 9.1- 9.2.2 before doing OS X of any kind. This will get your firmware in order.
OS X is picky about how the Hard Drive is formatted. Beige G3's started out with their drives formatted "Mac OS Standard" which is IDE format and only capable of properly mapping 10-15Gb of drive space. "Mac OS Extended" format is EIDE which CAN map more than 10-15Gb.
There are complications: Beige G3's had unreliable and fairly low quality ATA controllers on their mother board. These controllers can usually only see 1 ATA drive at a time. Most ATA controllers can see 2 and are considerably faster and more reliable. A new ATA controller can be had as a PCI card.
Processor wise G3's are considerably less stable (for OS X) than G4's and effectively useless when slower than about 466. I have an iMac 333 and won't be putting OS X on it until I upgrade the processor to a 466.
That URL leads to a VERY nice upgrade card for the Beige. It'll get you from 266 to 466 and you'll have a G4.
If it won't install on either machine there must be something else going on here. Have you tried installing 9 or plain old X.1? Is there anything non-default about your install process? Is there any "unique" hardware or 3rd party RAM involved? stay calm, we'll help you figure this out.
A system cannot have another OS installed on the same drive volume as it is currently booted from. Restarting with the "C" key down will start the machine from the CD and allow the install. Release the key when an OS splash screen or OS X "beachball" appears. If the machine refuses to boot from the CD, select it in the Startup Disk control panel and restart. If you get stuck at boot with a flashing question mark, restart with the option key down to start from OS 9 or simply wait for the system to "find" the Hard Drive. Back up EVERYTHING you want saved as OS X will most likely want to re-format your drive.