Congrats!
There are a few ways you can transfer stuff. You can get a CompactFlash card and a CF to PCMCIA adapter, pop the card into the Amiga 600's PCMCIA slot, format the card as and MS-DOS FAT-32 disk, then copy everything that way. Considering the price of 8 gig CF cards isn't too much, that might be easiest.
There are a few ways you can transfer stuff. You can get a CompactFlash card and a CF to PCMCIA adapter, pop the card into the Amiga 600's PCMCIA slot, format the card as and MS-DOS FAT-32 disk, then copy everything that way. Considering the price of 8 gig CF cards isn't too much, that might be easiest.