You might want to reconsider getting an old one:
http://www.guardian.co.uk/technology/blog/2010/jul/12/apple-time-capsule-recall-replace-fault
Netgear with AOL? Does AOL sell broadband service these days?
Usually with a broadband service like ATT or comcast you can use a router, however some of those companies sell a combo modem/router unit that can't be replaced with just anything (though they are usually 2WIRE, some Netgear's do exist).
Normally, you'd have a modem that connects to the ISP and to one computer. Then, you connect a router (like the Time Capsule) that routes the signal to multiple computers at once (some wired, some wireless, most are both these days). In that case you can use any router you want (usually) with the ISP's modem. However, as I said above, some ISP's sell a wireless service that is a modem/router built into one unit.
If you have that, you can't just replace it. You'd have to get the wired service, then use your own router (or, use another router in bridge mode, which can be confusing for some and not all of those combo units they offer make it easy).
All routers can be connected to with a device even if they aren't connected to the internet (although that isn't helpful), but I don't know if the TC can be used to backup to without it hooked to the net.
If it was possible, you'd have to disconnect from the netgear, connect to the internet-less TC, and do a backup.
