I bought the iPhone on PAYG. I don't use the phone enough to warrant the £35.00 per month, but I do use it all the time for internet access and e-mails.
You can not use your existing PAYG sim. You will be given a new sim with a new number.
You get unlimited internet access for the first year, after that it'll cost you a tenner a month for unlimited internet access.
If you opt for the contract then unlimited internet access is included in the monthly cost.