You do not mention the specs of your eMac ( CPU speed, how much RAM memory).
You may want to increase the amount of RAM in your eMac if it only meets minimum requirements.
Early eMacs could only take up to 1 GB of RAM.
Later eMacs could take up to 2 GB.
OS X likes memory RAM, so the more you have, the better OS X runs.
Depending on what version of OS X Tiger installs on your eMac, the last version of Tiger is OS X 10.4.11.
There is a combo updater package that you can download and install to bring your eMac to the last version of OS X Tiger.
If your eMac is either of the 1.25 or 1.42 GHz variety, you could opt to purchase and install OS X 10.5 Leopard.
This is the very last OS X version for older PPC Macs.
OS X Tiger is 6 years old. OS X Leopard is only about 3 years old.
This would allow you to be able to use any of Apple's latest and greatest iOS mobile devices at some point if you choose to do so.
Without knowing your eMac's specs, it's hard to advise.