Thing is a P3 is going to be hard to find so you'll also need to upgrade other parts than the MOBO and CPU -- what Video card did you buy and is it PCI, AGP, or PCI-e ?
chances are it also will not be able to be reused on a newer system (PCI and AGP are pretty much outdated and getting a new MOBO that supports them is going to really limit the upgrade and also cost more than just starting over (older parts get more expensive as there is a limited number of options available.)
IF you let us know what type of budget overall you will have and a bit of a detailed list of the parts you currently have we can put some suggestions together. ( ie. chances are you might be able to reuse the Mouse\keyboard, DVD drive,Monitor, possibly the HDD if it is worth it (a new 500GB. drive runs about $40 and is much faster than the old 120-160GB. drives), Case and Powersupply might be reuseable but Powersupply is probably under powered for what would be needed for gaming so might need replacing depending on the type of case you have. other than that the rest of the parts will probably need to be replaced -- PIII CPUs just are not good for games like morrowind etc. and the 1.9Ghz. spec is probably based on a PIV CPU not PIII ! --
Fortunately pricing has really come down so it is a good time for upgrading but we'd need to know a budget to suggest the best options at that price point. Another thing is do you have the windows installation disks from the old system or will you need a new copy of windows as that will add to the overall cost and needs to be considered.