Ooh, ouch. Yeah, the older G4 iMacs used the card you bought--the expensive, hard-to-find "regular" AirPort card. The later ones--which you appear to have, if it's a 1GHz model--use the newer, relatively easier to find, and faster AirPort Extreme card.
That's kind of on ziggyonice, although it's an understandable mistake--I'd forgotten that the later ones used the newer cards myself until I checked EveryMac. An article, for future reference:
http://www.everymac.com/systems/app...imac-g4-how-to-upgrade-airport-bluetooth.html
As for the issue at hand, yes, if you get the correct card--the Airport Extreme one pictured--that will definitely work with your wireless router. Wireless is, thankfully, standard, so regardless of the model/manufacturer of the router your iMac will be able to connect to it. You'll also likely get all the speed necessary out of said card; if you have an "n" router you won't be able to connect at maximum speed, but unless you're transferring data from one computer on the same network to another even "g" wireless will be far faster than your internet connection.
Bottom line, get the right card and you're in business once it's installed and the antenna cable is plugged in (harder than it sounds--I'm surprised at how easy it is to think you've got it connected when it's not quite fully in). The good news is the resale value on those old AirPort cards is very good, since they're the only wireless option for older G4 iMacs and older iBooks.
Heck, I was wishing for one myself for my parents' 700MHz G4 iMac which, unlike yours, DOES use the old cards.