Do something that will provide value, either to your community or to your school. Seriously, you can touch every technology you need or want doing anything at all, but if you create something that will benefit others, you'll be doing a lot more than writing a sterile app submission. It's also much easier to get behind something that has tangible results. Sure, all of the following have been done before, but there's always room for a local contender, and apps like this can get popular quickly. As to the database, just use an XML flat file. It's certainly not desirable or cutting edge, but you can do anything with it and that's how they did it back in the stone age!
Try something like the following:
- Study group meetup - allow students to create and search for study groups
- Community Service request - allow members of the community to ask for things from students (anything from needing help mowing a lawn to tutoring a high school student)
- Class-specific blogs - similar to the first one, but instead of focused on bringing people together, it would be focused on taking the people already in a class and giving them a platform to communicate and potentially discuss (maybe more of a forum) the class itself.
You could easily go crazy with any of the above, but just knock out the essentials, and knock them out in pieces. My biggest advice is that you develop this iteratively and focus on the core functionality BEFORE adding any fluff at all. That's the lesson you need to learn the soonest. Google "Scrum" and follow the simplest form of it you can grok.
As you reach certain milestones of functionality, post some fliers advertising your super-cool site to get some traffic and momentum before your deadline. Another great idea is to blog (on an already established blog engine) the entire process and solicit feedback on the features from your community. You probably won't be able to do most of what is asked, but just doing that will be a fantastic experience and will positively impact the few features you do decide to focus on. Advertise early and let the community help shape the result.
The process you take is at least as important as the result. If you work Scrum into this and develop this openly, involving the community from the beginning, you'll be on a really good path for your careers.