802.11b/g operate in the 2.4 GHz range, while (I think) 802.11n is in 5 GHz. You likely have Wireless-G capable cards in both your laptops, which can handle 54 Mbps (the average "high-speed" internet connection is 2-7 Mbps). Unless you plan on streaming HD video over wireless, or transferring multi-gigabyte files, an 802.11g router should be fine for all home office purposes. You can get a Wireless-N router now, but it is likely that your computers will only support G speeds (the N router should be backwards compatible).
Lack of privileges will probably keep your work laptop from being able to print (and may even keep it off the wireless network). You will have to talk to your IT department, and they may be able to install the appropriate drivers there for you to use at home, or they can boost your privileges for a day while you go home and install it (corporate policy may forbid that
).