OK, there is a whole lot to master here to get a good functioning controller. I might suggest that you buy one of these. It has every thing that you need to drive a motor except the Micro part.
http://www.pololu.com/catalog/product/711
Get you micro together and running on a carrier bread board or what ever. Then you can start the development work. As you noted surface mount power devices take a bit of effort to deal with the heat. That slug is very important to the performance of the device. Yes it has to be soldered to the board and additionally there should be many via's to transfer the heat to the bottom PCB layer. Being a ME it might be more beneficial to focus on the drive and control algorithms. Let the EE's do their job and make the boards.
Focus on the motor and the mechanical system. MOTION CONTROL. Today the micro controller is taking over the world. A ME today can not ignore the EE and control part of systems any more. You have to be able to walk the walk and talk the talk with the other members of a development team. This project is a good study. Note that you have chosen brushed motors. After you run the course on this you might what to focus on brushless motors. You will probably be seeing many of these in industry. There are many brushless development systems available. Though they cost a couple hundred dollars. Don't forget to take a look at stepper motors also.