We still have a 2005 eMac in limited service. As it maxes out macOS 10.5 "Leopard," new software will be nearly impossible to find. If it has the 1.42Ghz processor it was the best eMac made. Officially, it uses a maximum of 1GB RAM. Unofficially and with the right RAM modules, it can do 2GB RAM. Ours, bought in early 2006 as a refurb, has been running just fine for over nine years with 2GB Ram from OWC.
If you plan to use it on the internet, don't delay in getting TenFourFox. Its developer will be stopping work on it this year.
That browser does not support plug-ins so there is no sense in worrying about web videos. It won't. No Netflix. No YouTube.
Before doing anything else, and especially if you think you will spend money on it, I recommend verifying the model from the configuration code, the LAST THREE characters of the serial number This was copied from a now-defunct Apple support page:.

If it is not the excellent and reliable 2005 but instead the previous eMac (USB 2.0) with 1.25ghz or 1.00 ghz processors, it has a fatal and irreparable logic board flaw that, if it hasn't yet manifested, will.
To find the serial number, open the optical drive door:
