All eMacs were PowerPC G4. The earliest could only upgrade to Mac OS X 10.4.11. Only those with 1 Ghz or higher (800 Mhz or less are less), can upgrade to 10.5.8. Upgrading to 10.5.8 meant the loss of Classic, but not booting into Mac OS 9, if that was supported:
https://discussions.apple.com/docs/DOC-1757- tells you which machines could boot 9 and use Mac OS X 10.5.
https://discussions.apple.com/docs/DOC-2275- tells you more about upgrading to 10.5.
PowerPCs will always have trouble loading the latest websites, as there is no Silverlight for PowerPC, and you probably need to look at these solutions for Adobe Flash:
PPC max out at 10.5.8. Java on 10.5.8 is very limited:https://discussions.apple.com/docs/DOC-6491
To get better web browsing capability, migrating to an Intel processor machine is recommended:
If you have an Intel, you at least can upgrade to 10.6.8, which is still limited in terms of Java, but a little better:
If you have at least an Intel Core2Duo or Core i3, i5, or i7, you can upgrade to Mac OS X 10.7.3 or later, but only after checking your software compatibility with this tip:
10.7.3 offers both the latest Java and Flash support to date, and thus will not have trouble browsing any website except the few that require Windows, which can be added through this tip: