Getting your OS 9 machine to talk to your Classic should be easy, you can use good ol' EtherTalk (AppleTalk over Ethernet.) I have run into a bug where the older Mac running System 7 will error out when trying to connect to the Mac OS 9 machine, but it does work fine the other direction.
To network your Classic to your Modern Mac computer (or PC, UNIX, or Linux machine), it might be easier to just get yourself an FTP program for the Classic (such as Fetch), and then get something like ftpd-enable for your OS X machine. ftpd-enable is just an Applescript with a menu bar that allows you to easily turn on or off FTP on your 10.7+ Mac. I think in 10.6 or earlier, it's just a check box in the Sharing preferences. It's since disappeared.
That's how I network my IIci and MacBook Pro.
To network your Classic to your Modern Mac computer (or PC, UNIX, or Linux machine), it might be easier to just get yourself an FTP program for the Classic (such as Fetch), and then get something like ftpd-enable for your OS X machine. ftpd-enable is just an Applescript with a menu bar that allows you to easily turn on or off FTP on your 10.7+ Mac. I think in 10.6 or earlier, it's just a check box in the Sharing preferences. It's since disappeared.
That's how I network my IIci and MacBook Pro.