Is an iPhone handset cost included on the pay monthly cost?

I'm thinking of buying an iphone and comparing prices on http://www.omio.com/phones/apple/iphone-5s-32gb/deals

will the handset cost be included on the pay monthly or will I have to pay for the handset cost as well as pay monthly?

Depends on the plan you choose. Some offer the handset for free, others tell you to pay a certain amount upfront.