I want to stress that you have full artistic licence - feel free to go crazy and we can iterate.
Go for a design full of character - if that means creating an animal character - like the twitter bird, or something else - then go for it! The app is for students, it should be playful :)
Be bold with your designs - Facebook and Twitter border on dull designs, and Facebook is over-cluttered.
Keep things simple, bold and bright. Play around with font, both in terms of style and sizing.
There exists a trend at the moment with cartoons. Apple and Slack, among others, have both used this to good effect. However, feel free to experiment with different styles, Cartoony (Apple/Slack) and Clean (Airbnb).
Ask yourself, would you be attracted to your own design if you saw it in the App Store for the first time? If yes, then we're onto something :)