As the LG KS360 does not have WiFi capabilities, you will have to pay for the internet you use on your phone.
However, you can now get generous data packages with all network providers that will probably give you more MB's than you will even be able to get through- essentially making your internet "unlimited".
You should check out the various offers around at the moment to find out which one is best for you, as you will of course need to take into account how many minutes and texts you will need (if you are getting one of the bundled packages, which is how much networks are selling data packages these days").
Most PAYG packages will offer between 400MB to 2GB per month for between £10 and £20 a month. With this particular phone, the internet technology is 2G, which will be fairly slow to access pages, so I wouldn't imagine you would be able to get through more than 500MB in a month.