I have never heard of putting a fuse into an RC power system. There are lots of negatives, and frankly no positives. Does your professor actually know anything about RC planes?
As for your questions, I have one- do you have a voltage limit? If not, you can go pretty big on your voltage with a low Kv motor and still stay under 15 amps. That 500 watt idea would require 33 volts from your battery to happen for example. If there's not a voltage limit, I'd say this is a very poorly designed assignment. If you are allowed to go for ridiculous voltages, that obviously will impact your battery and motor choice. If your prof has his head on straight, there should actually just be a watt limit on the project's power system. That will be easy to test with a cheap watt meter and would allow you all lots of leeway on how to design your power system to work well with your airframe. The speed controller is just a gas pedal. Once you pick your motor, you just choose one that can handle the power system you are using.
With some answers on the voltage question, expected flying weight of the plane, whether or not brushless is allowed, and seriously, what is your professor thinking requiring a fuse to be used, we can give you more help.