I think from what you have said this would be totaly perfect for your situation.
http://www.dsl-warehouse.co.uk/product.asp?pr=DG834GT-WG111T
It's a dsl wireless router with 4 ethernet ports and wireless capability of coarse these netgear routers are VERY populer there will be plenty of people including myself to help you here if you have any problems installing it altho you prolly wont.
What you get for that is the router as mentioned a ethernet cable which you can connect to your pc via the ethernet port you mentioned your pc has but you've never used.
But also what your get there is a usb wireless dongle which after setting up router just connect the usb device to your laptop and enter the wpa pass key etc and your laptop will be online as easy as that.
Basicly if you do choose to buy this when it arrives connect the router to the dsl phoneline cable thats currently in your current speedtouch modem connect router to power cable and plug it in and connect ethernet cable which will come with it to router and to pc's ethernet port.
Then after thats all connected and its powered up insert the cd that came with the router it will bring up a auto install wizard and just follow the instructions. It will ask you for simple stuff like your isp's user name and password etc. Make sure when you come to setting up the wireless part in the wizard you select "wpa encryption" if you dont any naighbers could gain access to your broadband.
Again theres not much more to it apart from that really its pretty easy to follow the automated wizards instructions. However if you do have any problems u can always just reconnect cables etc to speedtouch modem come back here and tell us with as much info as possible the problem you've encountered and we'll try to help.
Oh yeh thats also a point i just remembered netgear have a freephone helpline you can phone if you have problems installing there devices too it will be printed on the box.
Blackmesa8