I am an Electrical Engineering student and minoring in Physics and Math. The minor in Physics and Math is because I like them both. It just so happens that my University (UCF) only requires 6 more credit hours (two classes) of upper level math courses beyond your Calculus / Diff Eq track. So, it is quite nuts for an EE or CpE NOT to get the math minor since you have to do all the math anyway!
That satisfies my curiosity for math. Even if you don't want the minor, you can still take upper level math courses that will help with your engineering. Classes such as Linear Algebra / Elementary Matricies and Applications of Complex Variables are really good math courses. A Physics course I would suggest that is very good for Engineers also is Intro to Theoretical Methods (will help problem solving / I don't know why this is a PHY courses as it is darn near pure mathematical).
I was torn between CpE and EE for a long time... but as it was stated, they are very close to the same thing. At UCF the difference is about 5 courses. If you want a more programming aspect or want to become more of a software engineer, go with the CpE. If wireless communications or power supplies are more your thing, go with EE. The fact of the matter is you can really do anything with the two... or just double major if you have an extra semester or two.
As for HAM Radio, I think it is highly benificial to the Engineer, but that is because I am a General Class operator. Before I even started engineering classes in college I was building my own recievers, transmitters, keyers, ect. All of my knowledge gained from HAM Radio and the 'old timers' in the club I belong to has made my Circuit Analysis courses mostly repetative and boring.
Then again, I have met many engineers who don't know a thing about ham radio and have no desire to become an operator. So, it all hangs on you. Go to
www.arrl.org and look up the local clubs. I believe there is even a page off that website that will get you started.
Hope this long post helps.