Although there are more options than I will give I will give IMO the cheapest and easiest ok?
OK, if it has a LAN port you have one main choice: (there's a second but i'm not 100% sure so don't want to say)
You need a wireless router: Something like:
http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&category=3706&item=5738902394&rd=1
CHeap ones start at £40 or so and rise to £100 plus. If you only intend to use within your house, almost all will have a strong enough signal, cheap or not. Good makes include D-link and Linksys (although I am a Linksys fan I had a problem with one before although we use them fine at home)
If you don't have a LAN port on your modem you need to replace this modem as it can't be easily networked: (I know it can before anybody corrects me)
Then you would be needing something like this:
http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&category=3692&item=6731160371&rd=1
This has a built in modem and both the above allow cabelled connections. They just give you an idea hopefully of what you are looking for.
Speed is another issue, there are two major standards, b and g. b is 11mbps, g is 56mbps, your internet is around 0.5mbps, i.e. whichever you get it doesn't matter if you only use it for surfing the net. However, as most stuff is g these days and it's backwards compatible, go for the faster g.
You may also need to buy a PCMCIA wifi card (make sure it's b/g compatible as the rest of your system will be) for any laptop without a wireless card. Yours already has one.
Any more questions before I go to bed? (have to go to Harrogate tomorrow)