Its much easier (and cheaper) to do these things on an Amiga 1200. If you really wanted this experience on an A500 (without spending a fortune) I'd suggest some extra ram and a HD, then use the serial port to run PPP to another PC (Linux/Win?) - this would give you TCP/IP networking without the expense. Browsing the web still won't be fun, or pretty though.
I use iBrowse on my A1200 (50Mhz 68030, 2 Meg Chip, 16Mb Fast, IDE HD, some weird multiscan resolution) and it's perfectly usable. Not the quickest and not all sites work due to lack of Java / CSS - but, it's an enjoyable experience.
However, if you like classic style hardware but want more power, check out NatAmi (
http://www.natami.net/).
Finally, welcome to Amiga.org - great to have you onboard!
Steve