I'm using the Netgear DG834G v2 here, and it's a nice piece of kit......wireless works anywhere in the house, on my laptop, nice and quick; speeds by wire are decent, and it's easy enough to configure.
Netgear aren't brilliant with firmware, but I guess you can't have everything......mine's still running on a relatively old firmware, because I know everything works with this version, whereas it doesn't with the newer versions I tried.
To answer a few of the original questions, there won't really be a speed-difference between routers and, if there is, you won't notice it; and yes, you need a wireless modem-router. And then, when it's all set up, you can keep the current wired-modem as a spare, since the wireless modem-router will do the job of that aswell...