Using Arduino type DIY platforms is becoming very common in Rapid prototyping design, but they do have significant drawbacks. To over come them:
Develop a robust requirements document based on VOC (Voice of the Customer). This I believe is the most critical next steps. In corporate all the critical user testing feedback into the requirements document. (Scope)
Determine a realistic budget based on expected price points. This is key in determine parts selection, resource selection, etc. One could use an expensive FPGA or inexpensive micro controller to achieve the same end result. What is important is that not to overshoot the budget. (Cost)
Determine the time to market. Once again this will impact your component selection, resource selection etc. (Time)
After there is a good understanding of Cost, Time, and Scope (Also know is the triple constraints) then start working on product design.
Electrical design: PCB design, electrical component selection (both electrical and mechanical), testing, manufacturing, compliance to regulations etc
Software design: Operating systems, software development platforms, software testing etc
Mechanical design: Component selection (both electrical and mechanical), mechanical testing etc. Mechanical engineers work closely with electrical engineers in most cases.
Tool selection: This includes any software for PCB design, software development, Mechanical CAD tools, any many more as it relates to finish product.
User Interface Design: If the end product has significant user interaction then it is important to consider Industrial Design into the design process.
Design for manufacturing and testing: IMO this is very important step. Understanding the capabilities for the manufacture and design according the capabilities. If the manufacture is required to special equipment this will drive the cost of the product limiting the success.