You should get your checkout crafted with the Payments Standard first. Once you have the checkout working fully with Payments Standard then adding the option to be invoiced instead will be much easier.
The extra checkout will consist of a form and a new confirm and thank you page. The checkout form will gather the user info, then post to the new confirm page. The user will confirm the details then be taken to a thank you page. On the confirm page you are just going to record the details into your database and indicate that the order has been invoiced.
Please post back with any specific questions that you have about any part of this.