Need Help Choosing an AirPort Solution for Home Network

What is the benefit to switching to wireless in my situation? I'm guessing that I would not have to hard wire my Macs to the router, and would be using the built in Airport to receive the broadcast signal.

That's correct.

The printer, I'm assuming, would have to be hard wired to the router because it is Ethernet

Also correct.

let me know if I should go with Express or Extreme.

AirPort Extreme. The AirPort Express only has one Ethernet port and it will be used to connect to the cable modem. Since you need to also connect your printer using an Ethernet connection, the Express would not provide this functionality.

but what does that speed hve to do with the speed of my cable connection?

There are two types of wireless "n" signals. One operates at 2.4 GHz up to a speed of about 130 Mbps. The other operates at 5 GHz up to a speed of about 270 Mbps. The AirPort Extreme will broadcast both bands and your Mac(s) will automatically connect to the best signal quality based on their location in relation to the AirPort Extreme.

Chances are, the Internet connection supplied by your provider is perhaps 10-20 Mbps. As you can easily see, the AirPort Extreme is capable of much faster performance than your service provider can supply. In other words, if you are connected to the Internet, your connection speed is going to be limited by your service provider....not the AirPort Extreme.

since the AirPort Extreme transfers at such a fast speed, does that mean that computer-to-computer file sharing will be faster than my old Netgear RP 114 that ran at Ethernet 10Base-T/100Base-TX?

Yes. Wireless on the AirPort Exreme will run faster than the Ethernet connection on your old router. Speaking of Ethernet, the AirPort Extreme has Gigabit Ethernet ports....1000 Mbps compared to 100 Mbps on the Netgear. Yes, that's 10 times faster.

Make sure that your Ethernet cables at rated for CAT5e or CAT6 to take advantage of the higher speeds.

So files transfers from device to device on your "local" network will be much, much faster than before.