What kind of initial patenting costs should we calculate?

Both of the previous answers posted by Steven and Andrew are very well written and provide very helpful and useful information, particularly with regard to the details of the specification and the overall process. To touch further upon your specific question regarding what are the initial costs, including costs to have an initial assessment, as a rule of thumb (without knowing any specifics), one can generally budget and expect to pay the following: approximately $600+/- for an initial prior art search and assessment (opinion); approximately $5,000-$7,000 for patent application drafting, preparation, and filing; and approximately $125/drawing for each high quality patent drawing of the patent application -- all depending on the complexity of the technology. As correctly noted in the previous answer, preparing an application involving a more complex technology takes more time and effort than preparing an application involving a simpler technology. The noted prior art search and assessment (opinion) as to patentability would be the first step the process, and would serve to help in your decision as to whether to proceed with a patent application.

In moving forward with a patent application, one can also expect to pay the initial filing fees of the United States Patent and Trademark Office (USPTO) according to its published USPTO Fee Schedule, which is located here: http://www.uspto.gov/learning-and-resources/fees-and-payment/uspto-fee-schedule

As an example, for an electronically filed utility-type non-provisional patent application with three independent claims, the USPTO initial fees for a Micro-Entity would include: a Basic filing fee of $70.00; a Utility Search Fee of $150.00; and a Utility Examination Fee of $180.00. If a provisional patent application is filed (instead of a non-provisional patent application) in this example, then the initial USPTO fee for a Micro-Entity would only include a Basic filing fee of $65.00. (There would be no Utility Search Fee and no Utility Examination Fee for a provisional patent application filing).