I'd forget about using the internet on any 68k for anything more than a mild curiousity, its far too slow and they don't support a lot of the stuff on most websites these days anyway.

It depends - an Apple IIe card will allow you to run Apple II software, but an ethernet card will allow you to connect the LCIII to your ethernet LAN (i'm assuming you have one) and transfer files, muuuuch faster than over LocalTalk. Furthermore, with an ethernet card you can do more things than you can do with LocalTalk, for example you can connect to IP based AppleTalk servers (such as Mac OS X systems), or install DAVE and even share files with PCs.