I would recommend SolidWorks. It is easy and intuitive to learn. Also, SolidWorks Electrical was just released, which could help with the robotics. This allows you to create schematics in 2D and then it combines this with a huge library of 3D parts so you import the 3D parts into an assembly and it knows how all of these components are connected.
andres_900 has posted a useful link to the YouTube SolidWorks videos. And these videos explain when and where you would use certain features of the software as well as tutorials on how to use it. Tutorials and what other users are creating in SolidWorks is posted on the SolidWorks teacher blog available at:
http://blogs.solidworks.com/teacher/.
Besides the content online you can find several books on amazon. If you get good at it there are also many certifications you can take.