eMachines would often change the motherboards throughout their production of a single model. I had an eTower (a long time ago) that shipped with one of six different motherboards. Hopefully you can lookup the model number and serial number to determine the exact type of memory to purchase.
Many of the eMachines models have very low limits to the amount of memory you can install into them. I know this next statement may sound a bit frightening, but I'm going top throw it out there anyway... You may want to look into an operating system that will allow you to maximize your hardware to meet your end goal. If all you need is a PC to run a browser to surf the web and read email, XP is way overkill for your needs. You could easily run a flavor of Linux that will service all your needs and do it with way way less hardware. I just re-purposed a Neoware thin-client that had a 300Mhz processor with only 128M of ram. Running "Damn Small Linux (DSL)", the entire OS takes up 50Mb of space on an old USB thumbdrive. The performance is way faster than a 1Ghz P3 w/512M RAM trying to run XP... just a thought. DSL can be booted from a Live CD so that it can be tried on the PC without making any changes to your existing XP environment. Downloadable and free at -
http://damnsmalllinux.org/Hope this helps...