Certainly: the beige G3 stands at the summit of the old world Macs, and as such has a lot to be said for it tinkerer- and collector-wise. Were I you, I'd look for a Beige G3 333MHz tower. Great machine: very, very reliable hardware.
Any Beige G3 can be readily upgraded to a 400-500MHz G3 via a ZIF processor transplant from a Blue and White; there are also third party G3 and G4 ZIFs available, at up to around 1GHz, but I am not sure if that is worth the trouble and expense. A 400MHz G3 processor will not set you back by much ($20?), and the machine could then most likely be overclocked to somewhere near 500MHz. (You have to overclock, by the way, even to move from, say, 233MHz to 266MHz, but the beige G3 is the easiest of all Macs to overclock. The processor speed is controlled by jumpers on the logic board, so it's mostly a matter of moving jumpers - the instructions are all over the web.)
The other advantage of the later (333MHz+) G3 ZIFs is that that have a 1MB level 2 cache rather than the 233-300's 512 MB cache. Much better.
Also, a Radeon 7000 PCI will work just fine in a beige G3 - in fact, in most any and possibly all PCI Macs. The Radeon 7000 will actually run even under System 7.6.1 with working acceleration (requires installation of drivers, most readily available from
www.system7today.com), so you can certainly run it under OS8 or 9 on the G3 (the beige G3 requires 8.1, as I recall). Or indeed, run it under OSX.
Your monitor will be perfectly happy attached to either of the two video ports under any Apple OS the G3 will run, or you could go with a dual monitor setup. The machine will, or should, automatically start up the monitor on booting, no questions asked.
With a card such as a Sonnet branded ATA-133 drive controller, you can put a massive ATA drive in the machine, which will work fine in OS 8, 9 or X.
For tinkering purposes and on the drive question, however, the G3 is an especially good machine, because it has both (albeit slow) SCSI and IDE already on the logic board. You can speed it up a bit with a SCSI or ATA drive controller and drives, but that would be maybe another $30-$40 spent if you don't already have the hardware lying around.
Older versions of Yellow Dog Linux are said to run well on the Beige G3s also, but I can't speak to that directly.
Best of luck with it. I just got a 233 MHz G3 tower, and have managed to find a 350 MHz G3 zif on EBay, shipped and all, for under $10. It's an IBM chip, which are supposed to be a bit more amenable to overclocking than the Motorolas. I'll see if I can get it up to 450MHz when it arrives. It'll almost certainly do at least 400; 450 may require a fan.