I can't really think of any other way you can achieve what you want without implementing Ethernet and TCP/IP on the classic or SE30. If the options were available to you, the simplest way of doing it would be to hook up a modem to the Classic and TCP/IP or Open Transport and get a dial up connection to an ISP. If you wanted to use your existing connection, you'd have to put either machine onto Ethernet and hook that into a hub connected to your router.
If you simply wanted to share files between your Ethernet/internet machines and localtalk ones, your G3 Powebook 'may' (depending on the model) be able to act as a gateway machine between the two as from memory the G3 Powerbook has both ethernet and serial connections. Ethernet could connect to the ethernet machines and serial to the LocalTalk machines switching between them in the AppleTalk control panel.
There's a number of ways to go, which one is right depends on what you want to do.