Any modern laptop will do. Celeron based from about £550, Dell do a centrino latitude for just under £800 (my wife has oen and it's not bad at all)
Kit: Ideally an ethernet ADSL modem/router/wireless access point. Plus a PCI wireless NIC for the PC. Plus, if not a centrino laptop, a PCMCIA wireless card. I would suggest getting the kit from the same manufacturer. I have a Netgear WGR614 (modem/router/WAP) and a Netgear WG511T PCMCIA card for my own laptop. Good kit, good instructions, great support in the UK, easy to set up and works well. Wifes centrino laptop finds the connection straight away too.