Wired depends on the adapter in your computer. 100 megs is usual, 10 on an old machine (max, it may well be a bit lower in practice) Might get a gig if you have a fancy card.
Unless it's an old 10 meg ethernet card, your broadband connection will be a lot slower than the network connection (unless you have access to a damn big pipe); mine's about 7 megs. The router's not going to make any odds as to whether you can use BBC iPlayer.
The only thing I would say is that ADSL2 may be on the way so it'd be worth checking the router can be configured for this.