Hi Scooby!
PC World are very customer friendly.
I got mine through Dell. They're great for customising etc. But I'm guessing you just want something standard for your son. They do have really good deals in PC World, so keep your eyes open.
You won't be paying for two internet connections. You may already have a wireless router with your curret broadband (BT provide this, for example) but some provider's don't provide wireless routers with their Broadband. So, you'll have to purchase a wireless router. You can get some cheap one's in PC World. It's just a once-off payment, and once you buy it you just set it up and use the internet on your PC and laptop.
Make sure the laptop is able to connect wirelessly before you buy it, although, most new laptops are.
Hope that helps.