Before ATI was bought by AMD they had legacy drivers posted for download. That disappeared with the buy-out. However, sometimes an e-mail to AMD support could get you old ATI drivers. Worth a try.
Adding VRAM to the logic board slot does not gain you much, and PCI vidcards may be easier to find. The only reason to bump the onboard VRAM to its max of 6MB is if you want to run dual monitors. As your can't use two video cards (the the "electron budget" comments below) the logic port port becomes important for dual monitors.
My first upgrade card for my Beige was a retail ATI Rage Orion 16MB. There was also an ATI Rage Nexus with 32MB, but the best card was the original Radeon Mac Edition 32MB that kahjot mentions. I have one of those too. It was expensive so was quickly superseded by the Radeon Mac Edition 7000 which was not as capable a card, but they tend to get advertised as "original" on some sites. You can easily tell the original RME from the RME 7000 if you have one in hand or have a proper photo. The RME has a cooling fan on the main processor heat sink where the RME 7000 has only a heat sink.
The last Beige-compatible card was the Radeon Mac Edition 9200 with 128MB VRAM. I have one in my most upgraded Beige but all is not perfect. The 9200 came out just as OSX was releasing and ATI had to delay release of the RME 9200 to decide what system they would support. They decided to go with OSX support and it was very difficult to get the card to work worthy of its cost under OS9. Even OSX wasn't completely smooth. As PCI on the Beige did not support Quartz Extreme technology the 2D performance of the card was rather kludgy. Dragging and opening windows was choppy, but OSX 3D games were pretty awesome. Descent 3 was stunning with that card.
Yes, you could enable Quartz Extreme with a hack but the hack commonly made other PCI cards work poorly or not at all. You plan to have other cards so I don't see that as an option.
Remember the PCI "electron budget." Technically the Beige's three slots combined can support 45W but in real life the limit is about 40W. Most vidcards are 25W so make sure your other cards don't exceed a total of 15W. The classic combo was 25W vidcard, a 10W FireWire, and a 5W USB. If your USB and FW cards combined are rated at more than 15W, consider a single combo card.
Speaking of USB cards, the biggest headaches we had "in the day" were USB cards that had the OPTI chipset. They seldom worked right in a Mac and often drew more power from the PCI bus than they should have. The most common troublesome cards were Belkin. Go for one with the NEC chipset. They have "NEC" prominently silkscreened on the largest chip on the card. Sonnet used NEC. I have a McAlly UH2-222 that is NEC in my upgraded Beige, and I believe Orange Micro cards also used NEC chips. If a card is not silkscreened with NEC, the odds are good it's an OPTI.
I glad you're here, Chris. Trips down Memory Lane keep my brain exercised!