The laptop I am answering this on was at one time an AMD K6/2-300, and it ran Windows 2000 Professional just fine. That's probably comparable to a P2 266 (MMX?). (I've since upgraded the processor to an AMD K6/2+ at 550 MHz, and it runs W2K much better 

 .) The minimum RAM is really 128 MB, and I have 192 on mine (the max for this laptop). Crucial and/or Kingston probably has RAM for your laptop assuming it goes to 128 MB or more. You may have to remove existing RAM to insert larger capacity RAM. I checked using Crucial's memory locator, but there are quite a few Thinkpad 600 models.
What video chip does that guy have in it? Mine's an ATI Rage LT Pro. You'll need to get drivers separately for that. Probably also true for your wireless PCMCIA card (I have a LinkSys WPC11 in mine.) and your wired network card if you choose to get one. My approach was to first do an installation and let W2K do the best it could with drivers. Then I added drivers as necessary to get all hardware recognized. Getting your LAN working first really helps.
Geez. I forgot to mention why. With W98, my laptop crashed at least once a day. Using W2K with its "built-in" hibernation mode, I now only reboot every week or two, and it's almost always due to MS critical upgrades or some such rather than a BSOD.
-cap