I do not want ideas like making a rat or a botnet as I'm interested more in preventing them than making them so please take this in mind when your writing your ideas.
Just want to point out, you can't fully understand something if you don't have the ability to understand the inner workings of the subject. Thus meaning it would be good if you knew how to construct malware to be able to prevent it. Not flaming at you, just pointing it out.
If I were you I would develop a database storing information about different students or whatever, and to be able to access this interface you would have to use a web based portal to be able to login. This itself would impress the teacher number 1 and number 2, because of your interest in security you could ouput the flaws such as the risk of an SQL injection.
By doing this you show something you love, and you impress the teacher, scoring good marks...
Method I would use in showing that your personal portal is vulnerable to the attack, Do netsparker, acunetix and nessus scans or whatever programs you choose against the IP of your portal. Construct a very neat report displaying the issue at hand, have a proof of concept and show how your remediation process would go to work.
Hope this idea would shed some light as I do not know what the scope of the school project is, but this is what I would do with the information you have provided us.
Edit: Sorry I think I made somewhat a mistake in posting this... I reread the thread and you said that the program would be using c++... You would still be able to create something similar I believe, having your program that is constructed in c++ be the application that is linked to the db in some way, maybe being the front end to display information about what the project is about, and if you click on "webpage" it links you to your portal...
I think if you use some creativity here you would be able to construct a bad ass project...
Pixel