The idea of paying a contractor in stages to make sure that the work is completed is something that is often done, and usually accepted.
However, I don't think that your staging will work. The tear out will work as a separate stage. Sequencing of the installation of flooring, cabinets, tile, wall board and paint don't quite work that way. For example, wall board needs to be done before installation of cabinets; painting is usually done towards the end. Tile is usually started with the cabinets, but might be finished last (think installation of splash guards, for example). (By the way, I worked in the construction industry before becoming an attorney.)
You may want to make the first payment after completion of the tear out; then percentages of payments for the total job in phases (like payment of 50% of the contract for remodel after the tear out when the job is 50% done). Remember to withhold a percentage (usually 10%) for up to three months after completion of the job to make sure the contractor will come back to make repairs.
With respect to purchasing the materials yourself, contractors usually hate that -- and not because they are trying to make a profit on the materials. Often times, homeowners select materials that the homeowner does not realize are not acceptable quality for a project, or not appropriate for the intended use. The contractor ends up responsible for the problem. You can suggest that you will go with the contractor to select materials, and pay for the materials when they are selected. Most contractors will be delighted not to have to advance the materials costs, and you will be able to make sure your money isn't wasted.
By the way, make sure your remodeling contractor is licensed (if your state requires it) before you enter into a contract.