What classes should I take and what classes should I avoid doing more than once for either Computer Engineering, Mathematics, or software engineering. Also, which is easier, Software or Hardware engineering.

Computer Engineers will do quite a bit of of computer science, but computer science majors will do very littlie computer engineering.

Comp Eng will involve not just programming, but designing physical hardware. Software Eng / Comp Sci is generally straight programming. If you are more hands on and interested in actually building tech, you'll want to go engineering.

You can have a career as a software engineer after doing computer engineering(CE). All you need to do is to take few programming courses and be good with algorithms.

But it is hard to get a break, if not impossible, in to field of hardware/chip design after getting a CS degree.

Coming to career prospects, software is ubiquitous and is running our lives. It doesn't show any signs of slowing down. At the same time custom hardware design is slowing. Software is now doing lot of functionality of what custom hardware used to do.

Eg. Most of the networking these days is done as software on generic machines/boards as opposed to custom designed hardware/routers/switches.

Have you checked out Robotics ? I haven't looked in detail, but I would imagine that has good amount of software as well as hardware.

Good luck ....

Each learning institute will have it's own curriculum for each major. You need to review the classes provided for each and then determine which aligns your passions. I'm sure once you review the curriculum for Rochester Institute of Technology. you'll get a good feeling of whats right for you.