I would buy an external hard drive. Then back up your MacBook Pro to a Time Machine backup (on the new external hard drive). Then, after you reinstall Mountain Lion (see http://support.apple.com/kb/PH10763 ), recover data from the Time Machine (the start up screens will walk you through that.
Many, if not all, software applications have hidden files in several Library folders. Unless you hunte them all down, you may have problems by just moving stuff over.
Anyways, the Time Machine method is probably the cleanest and safest way to move your stuff from an old Mac to a new one.