New
#11
You'd be better off with a new system with modern components. An old system won't simply do it especially with the slow processors. Finding a processor upgrade would be a pain and I doubt that an obsolete processor would even handle Windows 7 without any slowdowns. Your current Pentium III is likely a Socket 370/Slot 1 processor which has long been discontinued.
The fastest processors are the last P3 and Celeron which are both clocked at 1.4GHz. (Not worth upgrading)
ARK | Intel® Celeron® Processor 1.40 GHz, 256K Cache, 100 MHz FSB
http://ark.intel.com/products/27525/...he-133-MHz-FSB
You'll need a Slotket in case you're using Slot 1 if you're planning to upgrade the processor. You could upgrade your graphics if your board has an AGP slot. Anything like the Geforce 6200/6600GT or AMD HD3000/4000 series would be perfect but AGP cards are in legacy support so you'll have no new major drivers.
As for the RAM you should consult your board documentation, chances are that it supports around 512-768MB of RAM. Should be SDRAM or DDR1.