I have always had slow response for Internet on my Wii (the store, downloading games, etc). It is VERY slow and times out often.
I just got Guitar Hero 3 and am able to play online but it is VERY jumpy - I am definitely having a slow connection which is causing me major problems with trying to play online. It is impossible to play GH3 when it is jumpy - cause the notes are all over the place!
I have a Linksys router on a very fast Internet connection (8mb/sec rated, 12mb/sec via online tests). The router uses WEP and is physically sitting 3 inches from the Wii.
Any ideas are great appreciated.