Expeditions are helpful for gaining Dark Matter. There are occasions where you can also gain a small amount of Metal, Crystal, or Deuterium. And sometimes you even get some ships (Esp Probes, Light Fighters, nothing too big at least for me). However, you do risk the chance of being attacked by "pirates" and possibly losing the fleet you send, or getting sucked into a black hole and losing your fleet. You also might end up having something bad happen where it takes forever for your fleet to come back. Finally, there are a lot of times where you just get nothing from expeditions.
For ships to send, I usually just send some small/large cargo. I usually don't send anything too big in case they get attacked. And I only send like 3 or 4 ships at that. Again, you risk being attacked and losing your fleet, so it's risky to send a lot of ships.
Basically it's up to you to decide whether or not they're worth it. They are helpful if you want dark matter, or the small resources/fleet you might gain. It's also helpful for fleet saving if you're careful. If you do it enough, it can be really helpful.
I hope this is accurate and helped to answer your question. I'm sure someone else can correct me if I made any mistakes, and if you read about expeditions already, this should just be a summation of what you read.