There's no problem using a stock A600 on a local LAN. You'll want to get the extra 1M of CHIP RAM though. Even smaller stacks like AmiTCP 4.0 demo (I haven't switched to the 3.0b2 yet) take a fair bit of memory.
I typically just run the stack and Amiga Explorer. But, I've run an old version of Lynx and ncftp. I've also seen an old version of AMossaic that should run, but will probably be painfull.
