Hello and welcome.
The 600 even when expanded is probably too slow for browsing the web but it could be worth getting a PCMCIA network card so you can transfer files between it and a PC or browse aminet directly from the A600.
AmigaKit is a good source of hardware and they have both wireless and wired network cards that will work with your A600, these also include the software you'll need.
If you seriously want an expanded Amiga it's probably better to start out with another A1200, but be prepared to spend a lot of money on upgrades. 50Mhz 68060 card for example are now selling for upwards of £200, with 68030 cards often selling for more than £100.
Hopefully sometime in the future
Natami will offer an alternative to old hardware with loads of 3rd party boards hanging off it.
