Hooray! I now have my new Lifebook S6510 and my new Linksys WRT350N communicating via Wireless-N (802.11n) connection. The information that I got from Fujitsu Support (thank you, Wanda), was correct, although just a little bit short of being complete.
Apparently, in order to get a Wireless-N connection (Wanda said this was for any connection above 54 Mbps) you must be using WPA2 security. But in addition to that, what she didn't specifically tell me was that you apparently also have to use AES encryption, not TKIP. That wasn't too difficult to figure out, since I was convinced that the basic advice she had given me was correct; when I set up the router and laptop for WPA2/TKIP, and it still only connected at 54 Mbps, I just went ahead and tried AES, and it came right up at 130 Mbps.
My other concern was that I still have several other wireless devices which need to connect to this router, and which either can't do WPA2 at all (my Roku SoundBridge Internet Radio), or I would have to download patches or updates (the S2110, and a couple of Dell Dimension PCs). It turned out that this is not a problem, because the router is very flexible in handling connections. There's a minor confusion in terminology between the Vista and the Linksys router; Vista refers to it as WPA2-Personal, and Linksys calls it PSK2-Personal. Anyway, when PSK2-Personal is selected, the router will actually accept either WPA or WPA2 security. Then for encryption the router has either "AES" or "TKIP or AES". The result is that with these settings, the router is accepting a WPA2/AES connection from the S6510, and WPA/TKIP connections from everything else.
One other short note about software/firmware updates. I'm not sure that it was "necessary", but in the process of setting all of this up, I have updated the firmware in the Linksys router (to 2.00.17), the Intel wireless adapter (to 220.127.116.11), and the Marvell Yukon Gigabit Ethernet controller (to 10.28.3.3). Even if some of these might not be absolutely necessary, with something like Wireless-N, which is still pretty fluid, it's best to have the latest that you can get.
In addition to this wireless success, as I mentioned previously, the S6510 is connecting wired ethernet at 1.0 Gbps. With this setup everything is working just fine, and these higher wired and wireless speeds were one of the major reasons that I bought the S6510, so I am quite pleased.