Wireless router - will it work...?

[Snowsride]

My daughter and her husband have accomodation in the basement and ground floors of a large house - there are two other flats above them. They have a desktop PC located in the basement with a broadband connection and my daughter wants to access the internet from a ground floor room using a laptop that does not have WiFi capabilities.

Can we plug a wireless router into the PC in the basement and get a wireless USB unit for the laptop to enable communication with the router?

Is the signal strength strong enough to enable communication from one floor of the house to another and if so is there anything to prevent the occupants of the other flats, deliberately or inadvertently, connecting to the router? I assume it requires the remote machine to know the IP address of the router it is attempting to communicate with so I guess this is sufficient security?

If you can understand the above can you recommend suitable equipment? I have seen a Linksys Wireless - G Broadband router advertised which looks good value - is it? Also can it communicate with a VPN?

What piece of kit do we need for the laptop?

Help!

Thanks