You can still get the retail installers that will work with the eMac if you shop around.
Look inside the optical bay drive door and read the first 5 digits of the serial number to tell what will run in it.
The first two are of no consequence, the next three are important. It is in the format xxlast digit of year, week of year.
xx405 is the 5th week of 2004 release. eMacs with xx217 to xx317 serial numbers can only upgrade to 10.4.11.
eMacs with xx416 serial numbers and later all support Leopard to 10.5.8. Those in between may support Leopard, but only if they are 1 Ghz. If you don't know what speed it is, you may be able to look behind or underneath for the speed. If not, you can only assume you can use the retail release newer than the machine. Leopard generally needs 512 MB of RAM, where you can get by on 256 MB of RAM on Tiger if you don't use additional widgets or sophisticated software. xx518 to xx544 must use 10.4.3 or 10.4.6 retail. xx545 or later must use 10.4.6 retail. All others can use 10.4 retail. 10.3.5 retail and earlier are harder to come by, and with only going up to 10.3.9 doesn't support that many websites. If you do upgrade to 10.5 or later, you won't be able to install Mac OS 9 or use Classic. If you can't find your eMac Mac OS 9 installer you need to find someone who has one, as it won't use Mac OS 9 retail any release. If you must get 10.3 because of older compatibility,
only eMacs with xx344 or earlier can use 10.3 or 10.3.5 retail, xx432 or earlier can use 10.3.5 retail.
10.3 retail looks like 
10.4 retail looks like 
and 10.5 retail looks like 
.
None can say Upgrade, Dropin, or OEM.
