Lost Internet

I have recently converted to an iMac. It is connected--networked--via a modem and Linksys G router. The connection defaults to AirPort. Since the change I've been offline with greater frequency than with my PC. I don't know whether it should be connected via AirPort or, if not, Ethernet and how to turn off AirtPort for the alternative.

Might it have something to do with the router? I understand Macs use N versions.

What should I know about connectivity with a Mac that is different than with a PC?

Thanks.