I'm reluctant to post this because I don't want to dampen your enthusiasm. But I think it should be said.
Jumping from OS 9.x to OS X might be compared to jumping from Windows 3.x to 98 or even XP, and trying to update the 3.1 machine to handle it. If the problems turn into too much of a hassle, you might find yourself stuck with 9.
What's the speed of the beige machines' processors? I have an old blue-and-white (more green than blue) 350 megahertz G3 that had 512 megs of RAM when I loaded it with 10.2, Jaguar. It ran at half the speed or less with X as it did with 9.2, but it was usable. Even jelly-bean iMacs were faster. (The blue-and-whites replaced the slower beige G3s.)
Your 9.1 machine would have to run 9.2 if you want to run 9 in X's Classic environement, that is, 9 booted through X, not independently; that's not possible with 9.1. The update's free, I think, but there might be a firmware update required (if it isn't included and if the beige machines support it without jumping through hoops). Others might know more about this, and the info would be on the web, somewhere.
When I got my G4, the G3 went on permanent loan, more or less. But when I got it back a couple of years later it had a meg of RAM and had been loaded with Tiger. OS X was noticably faster than when I used it with Jaguar.
I'm no computer expert by any stretch, but FWIW and IMHO, upgrading beige G3s might prove to be an exercise in frustration. But if you can do the work yourself, it wouldn't cost as much as it would me. Other bottlenecks you'd run up against might be the bus speed and caches and so on, so you could hit the point of diminishing returns sooner rather than later and have spent a lot to get there. I haven't a clue about video cards.
OS 9 and X share a ton of GUI similarities, but they're a mile wide and only an inch deep. Under the hood, 9 is a steamer running on benzene. X is a BMW.
I run 9 and X in my G4, but trying to keep 9 as up to date as possible on the web is a hobby in itself. I use the very old browser but now rather insecure third-party WaMCom build of the Mozilla suite, 3.1, that can even run some Firefox-for-OS X extensions — Adblock, SmoothWheel and Mouse Gestures, for instance — and the WaMCom build is easily pipelined. I found that out only because I tried them.
JavaScript is the worst pain. It's 3 point something or other and will never be updated, so the doors on some sites are slammed shut and locked tight. And 9 constantly needs coddling to keep its boiler pressure up.
I have two 9 partitions, one being small that I use to keep the main partition running properly: I would never run 9 without Norton — Disk Doctor and Norton's Speed Disk defragger. Apple's built-in Disk First Aid for OS 9 is a bad joke.
But the Norton disk is long gone, so I have to run it and a couple of others from yet another partition with a stripped-down system (doing so is much faster than using the Norton disk, anyway). But accidentally running Norton on the wrong partition — OS X — is suicide.
The coddling required to keep 9 trouble-free and at optimum performance is as much an art as a science, and to the unitiated, each passing year would make it look more like voodoo than even an art. A rough comparison might be someone who learned on and has always driven a car with an automatic transmission suddenly years later being confronted with a stick. What's the third pedal? A clutch? What's a clutch?
Who remembers the pre-OS X need to "rebuild the desktop" and the problems that will ensue if it never is? More to the point, who cares?
Anyone know or remember the horror of extension conflicts and how to resolve them? How about Chooser problems? Wait! What's a Chooser?
The knowledge is leaking into space because it isn't needed any more. But I didn't have to learn 9 and X at the same time because I entered the Mac world with System 6, and later there was plenty of help on the net, as there is now with X. Any otherwise-easy fixes in 9 might put you completely off X, where such problems don't exist.
I keep 9 because I need it for my version of Quark that on principle I absolutely refuse to update. And 9 on the web has turned into a fun challenge.
But the fun is fading. Now 9 is even hobbling X running on a G4 because of such things as Photoshop 7. I won't update 7 because it runs in both systems. The present, not the future, is Intel, and Intel kissed 9 goodbye for good a long time ago. The G4 will run Leopard, but the beige machines were built for 9, maybe 8.6, to run on a chip older than the outdated G4.
But regarding OS X, one of the best series of books is the Missing Manuals. Mac guru David Pogue, who among other things has a computer column in the New York Times, wrote them, the latest book being for Tiger. Going back, there are editions for Panther (the beige machines might not be able to run Tiger) and Jaguar. There might even be one for System 9. But other books on 9 could be had if there is no Missing Manual for it.