Hello,
I have boycotted Linksys equipment due to their Windoze Superiority Complex(tm) and their equipment is pooly shielded to RF radiation (My ham radio gear picks up their hubs, whereas other hardware folks does not get into my radio).
You are going to want a router that has an option for an external antenna. The one I purchased is from Buffalo Technologies, and it will support an external antenna, and also has 4 or 5 local hub ports for wired machines & printers.
As it stands, your Airport Extreme 802.11(g) card in the G4 should work fine with the Linksys, as long as the signal makes it through the house. Ideally, you would have the wireless hub on the second floor, so that your radio signals don't have to travel as far. Depending on the materials used in the house's construction, your setup may or may not work.
Next question: do you need detailed help configuring the router? If so, please write back and let us know.
Christian