I'm using the version of Genesis that comes with OS 3.9 with no problems. I'm connected to my cable modem with a D-Link router/firewall.
It should be just a matter of knowing what the correct settings are for your router.
Does Genesis support DHCP? If not a router would be your best bet. Your router will get an address from your cable company using DHCP and then you can setup your amiga using settings defined by your router.