Based on my experience in IT consulting for large corporations, it's essential to have a high-level plan that outlines the work being done, the time it will take, the resources and the cost. On-going communication is an important element to maintaining a good relationship.

For pricing, we used hourly rates and we estimated it based on a costing tool for typical projects. However, since you're new, I'd say to come up with your best estimate and then add additional hours for any unknowns. Communicate that this is only an estimate and the cost will become much clearer when work commences.

Communication is key to your project's stakeholder. We provided weekly summary updates to the executive management on how the project is going, included the hours we've spent working and what we worked on, as well as how much costs have change since our original estimate.