Hello lanchar,
I just bought an eMac for my parents and upgraded the memory to 512mb (two sticks of 256mb)....
The first question you ask about the finger room..... You open the eMac "hatch" and the memory slots are right on top... Very easy to upgrade..
you can run a system test.....you need the first restore disc that came with your eMac.... read the instuctions on the disc... If you want to run the test overnight....You can loop the test by pressing the "ctrl" key and letter "L" at the same time
Good luck...