The problem with the A500 is the speed you can achieve through the native serial port with the standard 68000. And a 3.1 ROM is a minimum for graphical web browsing. Try adding a VXL030 or CSA Derringer 68030 board in the 68000 slot to speed up cpu cycles. These shouldn't interfere with the sidecar hardrive you may have, but check before you buy (stay away from MTec products, they interfere with DMA).
As far as the serial port goes, Individual Computers made a small amount of adaptors boards that fit in the 68000 cpu slot and add two a1200 style clockports. You can add a Silversurfer clockport fast serial card on one of these clockports (also from Individual) to give real fast serial access via modem. The clock port board may or may not be compatible with the accelerator. I have one and a VXL030 too but haven't tested them together yet. Of course, it is also possible to add a Subway USB adaptor to one of the clockports but I don't know if the drivers support it.
The most elegant solution is to add a real ZII busboard onto the side expansion port and use a ZII ethernet card to go broadband, but these are very hard to find and in that case an old A2000 would be a much cheaper way to go.
Oh, and don't forget that the Amiga native chipset uses chipmem to display images, so you're going to want to add a 2MB Agnus upgrade board (MegaChip or similar) or a graphics card (ZII only)...another reason to go right to an A2000.
