If your eMac model CPU is faster than 867 MHz, you have the option of either installing OS X 10.4 Tiger or try OS X 10.5 Leopard. If your eMac is a 1.25 Ghz model or better, you can search for the official Apple OS X 10.5 Leopard retail install DVD and install 10.5 into your eMac.
Both OS X 10.4 and 10.5 are long unavailable from Apple.
You need to look to eBay, Amazon or a website I found called Fastmac, to purchase an official retail install DVD of OS X 10.4 or 10,5.
The OS X 10.4 retail discs are black with a silver " X" on them.
OS X 10.5 discs have a purple star background with a black "X" no them.
DO NOT PURCHASE ANY GREY COLORED DISCS! These will not work!
Grey disc are machine specific discs that ship with a new Mac.
They will not work for any other Mac.