You should be able to upgrade your Katmai PIII processor. I believe they were all slot 1, so in order for you to upgrade to a 1 ghz CPU, you will probably need a slotket adapter which will allow you to put a socket 370 processor into a slot 1 mobo. The slotket adapters are getting harder to find, but you can also check the FSFT forum as well. You have a choice of getting a PIII 1 ghz or a Celeron somewhere in the 1 ghz range. Both are socket 370 coppermines and both can be found to run on a 100 FSB which your motherboard likely supports. The PIII 1 ghz also come in the 133 FSB variety but you'll have to make sure your mobo supports that. Also, if you have any desire to OC, you should get a 100 FSB CPU.
I don't know anything about Linux.