The Shuttle Bay is unlocked by research at Operations Level 8. This will unlock away teams assignments.
Away teams assignments don't have the biggest rewards, but they have some of the best because they are constantly going throughout the day, so they add up over time into quite a lot. As you level up, you'll unlock more and more assignment slots, so you'll have more going at once. They give you a nice place to put some of those officers that have been collecting dust on the side.
So the more assignments you have, the more officers you need to have available. You're going to have to balance keeping your most powerful officers on ships and keeping them going on the away teams missions, which can sometimes be a difficult choice.
For the away teams research tree, you need to have service awards. To get these you must complete missions. And they get expensive quick, so you'll need a lot of them.
From time to time, there will be away teams solo milestones and solo leaderboards. So while it might be tempting to speed up and complete away teams as much as possible, it is in your best interest to only speed up the ones where you feel like you need an officer for another away team mission or for a ship.