You are better off using System 7.01 or newer. I believe you can download
many more recent OS's from Apple (for free) up to 7.5.5 that will work on
an SE. There may be a way to make OS 6 work but I am not aware how.
I myself have an SE that I run both 6.08 and 7.5.5 on it. I use 6.08 for
writing and some old games. It is much snappier then any of the OS 7
versions. Then I reboot into OS 7 when I want to use the network. OS 7 is
slow on an SE so I suggest that you not use it as your main OS.
Both system 6 and 7 are small and will install on a zip drive. So if you
don't want to partition your internal hard drive you can have your SE dual
boot from a system installed on a Zip.
Be aware that if you ever upgrade to 10.4 (Tiger) on your G4 that none of
the system 7 versions will work with plain Appletalk networking anymore
(you need Appletalk over IP.) So I wouldn't recommend Tiger unless you are
prepared to jump through more hoops.
It is nice to here about others who still use an SE on their network. If
you have any questions or would like to discuss SE issues feel free to
e-mail me off list.