IEEE1394 Adapters are used for point to point connections only, You can hook up 2 computers via Fire-Wire ports. If you are looking for a network adapter for windows 7 go with a USB or PCI adapter.
Go to Linksys, Netgear, Belkin, or any other network adapter company you like and look at the adapters you need and see if they support Windows 7. You need to make sure you get the correct type you need (Wireless or wired) to hook up to your router.
You can use different companys for the router and the network adapter, Both need to be able to use the same speeds (IE: 802.11g or 802.11n or 10/100Mbps).
If you had a adapter working in XP/Vista you might be able to find the Windows 7 drivers for that adapter. But not all adapters have Windows 7 drivers.
If you have to go back to the old OS if every thing worked. Depending how old your PC is it could be better to stick to the older OS.