The most cost effective hardware evolution for a Beige is, one, add RAM (at least 384 MB total or max it out to the 768), two, install a high performance 7200 RPM HDD (yes, you are limited to 16.7 MB/sec on the motherboard IDE bus, but a fast HDD on it will be much quicker than the slow stock HDD), three, add a HDD controller in the PCI slot (an ATA-66 controller will do wonders for HDD speed), and finally four, add a PCI video card (a 16 MB Rage Orion is cheap and will add significantly to 2D performance).
For memory management, in the Memory Control panel set all to default except the fourth item, which controls memory tests at startup. Turn off those tests. You don't need them once you've confirmed that your RAM is working the first or second time. If you have enough RAM MBs, increase the minimum and preferred memory in your most used applications. I set the minimum at the suggested size and the preferred at some multiple of suggested (e.g., IE for Mac preferred memory set to 80 MB).
I wouldn't partition a disk unless I had to. If you're looking at disk optimization, try DiskWarrior to optimize your directories. I've found it had a greater positive impact on OS 9 performance than Norton's Speed Disk. If you don't have Norton's Disk Doctor, run the most recent version of Apple's Disk First Aid often.
Unless you're running a big CPU upgrade, turn off the Control Strip extension and control panel. If you are using the stock Rage Pro video graphics, set them (in the Monitors control panel) to thousands of colors, not millions and don't set the resolution above 1024. These adjustment will add to the overall quickness and speed of your Beige. If you prefer beauty to snap, ignore these video setting suggestions.
Although it is questionable as to whether or not virus protection is still needed for OS 9, if you can find a cheap or free copy, Norton Anti-Virus for Mac, version 7 was the last one for the classic Mac OS. It works simply and well, especially with a large memory allocation. If you can get it with a still functional Live Update feature, Norton still posts monthly virus definition updates for it. Most of the new virus update items are Macro viruses, which may or may not affect what you do with your Mac.