Going to be running space combat tomorrow for the first time.

The characters will all be on the same freighter, do they get individual initiative slots to act on, or is it just one slot for everyone on the ship?

They will be picking a fight with a small cruiser, the NPCs on that ship will all act in the one slot, so do PCs crews do the same?

It's up to you and your players, really. Having them all act in the same slot will simplify things a little, but it's not a huge deal either way.

Well the rules have players all in individual slots. It also works well in that regard as you would want someone to do a Fire Discipline check first before your gunners fire, or for the Co-Pilot to make a check to help the Pilot's next check. Your place in the initiative is often a very important choice to make on each round.

When I ran mine, they all had their own slot, but then they were all doing different things.

We had 2 in the weapons firing in separate initiative slots, one doing the flying rolls as needed (or declaring their maneuvers) in another, one running repairs in another.

They were fighting individual fighters, and each enemy had one slot to do what they could it.

But i guess whatever works at the time