A good starting point might be to use Lego + Mindstorm (or Lego + Arduino). You get to use various off the shelf mechanical parts and you get to re-use the Lego parts in your next project.
Yup, that's a fine suggestion, too. I used to do all my prototyping with Lego Technic pieces... Years later, when I needed parts that Lego didn't make (like for connecting servos or Arduino), I used Lego dimensions to create my own 3D printable (but Lego compatible) parts.