Hi! Quite a fun idea for a HW project :-)
You can install AmigaOS 3.1 ROMs in your A500+. I don't know what hardware requirements OS 3.5 and up has, but Workbench 3.1 should run fine and provide you with a current enough environment to run a TCP/IP stack and most web browsers available on Classic Amigas today.
As for the hard drive, if you can find a GVP A530 this would probably be your best shot. It's an external (sidecar) hard drive AND accelerator in one, with a 68030 CPU at 40MHz and fast-RAM.
If you're using dial-up, any old serial modem should do. You could also use a null modem cable connected to a PC, Mac or another Amiga connected to the internet and use that computer as a gateway. I don't know of any NICs for the A500+, but if there is one, I'm sure someone here knows about it.
Good luck!
