I suggest you do a search on this as there have been many of the topics over the last day or two.
A router is the best option using a built in ADSL modem. I use 802.11b (11Mbps) and this works over both floors (with excellent signal strength) from one side of the house to the over and should have a range of 120 metres. The faster technologies (802.11a or g) have a shorter range and are more secure. A simple network using the 'b' technology should only cost around £100 if your prepared to shop around and get differenet components from differenet manufacturers.
Therefore the router can be placed anywhere you like, though near a phone socket would be useful. The router could be connected directly via ethernet cable to the PC and then a wireless NIC could be placed in the laptop, or both computers could have a wireless card. Neither computer is needed for the other to gain internet access.
Hope this helps