Welcome!
First let's verify whether your eMac has USB 1,1 or USB 2,0 ports. There are eMacs variants with 1,1 and others with 2,0.
From your Apple menu, please do "About this Mac." When the "About" window appears, click the "More Info..." button. This is from one of our working eMacs
That launches System Profiler:
If the Model Identifier has the code PowerMac6,4 as in the example, your eMac has USB 2,0 ports. If the code is PowerMac4,4, it has USB 1,1 ports.
If it's 2,0, any USB 3 drive should be backwards compatible. My 2010 iMac with USB 2,0 ports is very happily backing up to an Other World Computing external drive with only USB 3 connectivity. Not completely sure about USB1,1 being compatible but I believe it is.
If you are looking at spending money, remember that a large group of eMac with USB 2,0 ports had a massive hardware flaw that is effectively impossible to fix today. One day they work, the next day they are dead. Those have the 6,4 code in Profiler and 1.0ghz and 1,25gHz processors. Affected units usually--but not always--fall in these serial number ranges:
- G8412xxxxxx- G8520xxxxxx
- YM412xxxxxx - YM520xxxxxx
- VM440xxxxxx - VM516xxxxxx
If your serial number is among these, I would not want to spent a great deal of money on the project.