By far the cheapest option is to add a BT socket upstairs and have a modem/router with 2 wires (one for laptop, one for PC).
It's really really easy to set up the wireless connection that you outline but it can be quite expensive.
Buy a wireless modem/router like this:
http://tinyurl.com/35bu7
(there are cheaper ones available - this is just the first one I encountered)
and for your PC, a wireless adapter
http://tinyurl.com/3l7eu
For your laptop, a "PCMCIA Card"
http://tinyurl.com/6vl89
After a bit of configuring you should be able to share your broadband connection between the two.
If you've not had broadband before it's imperative that you have (software) firewalls and antivirus etc. on the laptop and the PC.
If you use any p2p things or online gaming at all, they might need extra configuring afterwards.