I've recently brought an iPhone 3G, and I have no troubles connecting to my home wireless network (Netgear router), and browsing speeds are quite quick too. I think some people have trouble with the passwording and encrypting support between the router and the iphone, try turning passwords off and see if it works..
As for the screen, definately purchase something like
This and let that get scratched rather than the screen, it works like a charm for me! The only gripe I have about the iPhone is the iPod sound quality is as always for Apple only mediocre and I don't really like the sound quality...
Matt