I had a problem with XP. Blue screen. No previous good config nor restore point worked. Problems with the registry. I think it was some authomatic XP update. I had to format and reinstall the system. Same three times in a week.
I think you can use a 802.11b in a 802.11g network. G APs should send b signal but if the G AP is not good quality you will get very bad speed with all the hosts.
If both laptops have a firewire port, you can use it with a firewire cable (400Mbps). Fast and simple. Just configure the network (IPs).
You can connect 2 laptops with wifi in infrastructure (I don't remmember if this is the name) mode.