ClickFunnels integrates with Stripe, Paypal, and other types of payment processors, making it extremely easy to integrate if you take payments online for your services. It also allows for custom code to be inserted pretty much anywhere in a given page, which allows for you to truly customize your landing page, and even provide other checkout options like PayPal for your customers. You can also provide different price points and pricing options for your customers, built right into the landing pages.
Prospecting and marketing are all the things you do to get people into the first of your sales funnel stages. Note that stages are broken into two or more steps wherever possible. A demo could be called a single stage, but in real life it involves a lot of things: contacting the customer, sending reminders, doing the demo, and then following up. Whatever your own sales stages look like, the support you need in managing them will be the same.