I have been given the task to design a database to store a lot of information for our company. Because the task is rather big and contains multiple modules where users should be able to do stuff, I'm worried about designing a good data model for this. I just don't want to end up with a badly designed database.
I want to have some decent examples of database structures for contracts / billing / orders etc to combine those in one nice relational database. Are there any resources out there that can help me with some examples regarding this?
Barry Williams has published a library of about six hundred data models for all sorts of applications. Almost certainly it will give you a "starter for ten" for all your subsystems. Access to this library is free so check it out.
It sounds like this is a big "enterprise-y" application your organisation wants, and you seem to be a bit of a beginner with databases. If at all possible you should start with a single sub-system - say, Orders - and get that working. Not just the database tables build but some skeleton front-end for it. Once that is good enough add another, related sub-system such as Billing. You don't want to end up with a sprawling monster.
Also make sure you have a decent data modelling tool. SQL Power Architect is nice enough for a free tool.