It doesn't matter if you have XP-XP or XP-Vista, you shouldn't have any problems. The PC will need to have a LAN port/NIC/Network Card (all the same thing) installed if you want to network them. As this is a new laptop, it will likely have a wireless adapter already built-in, i.e. it will be 'wireless ready', plus it will have a LAN port. So all is there for you to be able to set up a wired network.
If you want to set up a completely wireless network and also share your internet connection wirelessly, all you will need is an ADSL wireless modem/router (about £50) and a USB wireless adapter (about £15, for the PC).
If you want to leave the PC wired to the router, then you don't need to buy the USB wireless adapter.