How does internet on a mobile phone work? What company would You recommend?

I am planning on getting the LG Cookie (otherwise known as the LG KP500) and am told it has "Quadband, WAP, GPRS" etc with this will I be able to get the internet straight to my phone - and where from? I have a Wireless Router for my PC so will it just run to my phone like a Laptop for Free? Or will I have to set up some sort of Contract and pay so much a month for it?

If I have to use a company and go on some 'Price Plan' what company would You recommend?

Thanks for Your help :]