The first thing you should be considering is how would you usually connect WorldPay to a .Net website. The fact that your site is Umbraco-based needn't complicate things.
Find a couple of articles describing integration into a standard .Net website and see if those approaches will work with your website. The only complicating factor might be defining a "callback" page, but then at worst you could just use a hard-coded URL.
Many questions like this assume that Umbraco complicates otherwise well-documented tasks. But generally an Umbraco site is still just user controls and masterpages or views and actions.
If you want to make the Worldpay configuration editable within Umbraco, that is another question completely.