Hello and Welcome!
It's sad to say but anything less than a 68020 might not do much good with networking. I'm not positive but I think the TCP stacks available require a 68020 or better. I know that AmigaOS 3.9 requires a 68020 so you'll have to find an accelerator board for those classic Amigas you have or else buy an A1200. It's easier to find good expansions for the AGA chipset Amigas since they're newer.