Surfing the net using an Amiga is possible, but not very pleasant on an Amiga without a graphics card. Try surfing on your PC with 640 x 480 and 256 colours :-)
Only way to get a graphics card on A1200 is to put it in a tower, together with a Mediator or a Zorro busboard. Only suitable option for a desktop A1200 is a Blizzard PPC with a BVision installed.
If you just want to be able to transfer software from PC to Amiga, then all you need is a PCMCIA ethernet card and some fast ram. A faster CPU wouldn't hurt either, so a Blizzard 1230 would be a good item to get hold of.