Since there hasn't been a first mission officially set I guess i'll start throwing some out there. If I know one thing it's action movies. Other people, please feel free to put some of your own ideas too.
1. After setting out from the Academy we are intercepted by a Hirogen Hunting Part* whose only mission is to kill and take trophies from the dead and show them off.
*The Hirogen are an extremely aggressive race from the Delta Quadrant. They can reach the height of over 9 feet and their physical strength is many times greater than that of a human. The Hirogen are easily identified by their body armor, it allows them to survive in the most hostile environments.
A powerful Nomadic species occupying the Delta Quadrant, the Hirogen are very predatory race. They travel in small ships carrying only two or three persons, seeking out other life forms in order to hunt them. They are obsessed with gathering trophies - usually in the form of body parts or stolen technology - in order to demonstrate their hunting prowess to other Hirogens.
2. After setting out from the Academy we get a distress signal from a crashed Starfleet ship. When landing we find out it was Kazon** that attacked the ship and sent it towards the asteroid. When searching for survivors only the Kazon are alive and then attempt to steal the ship and it's technology.
**Kazon; The Kazon are the first group of aliens encountered by the U.S.S. Voyager in the Delta Quadrant. They are an aggressive, humanoid race of space faring plunderers who have become one of the leading powers in the region. They are a race of warriors, split into many sects. Each sect is headed by a Maje. The number of sects changes `almost every day'. It is mentioned that there are 18 sects in total. The Kazon gained independence about 26 years ago. Since they encountered the U.S.S. Voyager they are very interested in the transporter and replicator technology.
Just a few I thought of that would be cool. I'am just throwing stuff out there, so please put something if you think it is good too.