Probably a stupid question, there's likely something obvious I'm missing, but I've yet to finish a mission because I keep getting to the exit system and not knowing just what I'm suppose to do.

I get there and it tells me that I have reached the FTL comm relay, and I can jump to the next system when my engines are charged. Then nothing else happens, and all I can do is jump around systems until the rebels catch up to me.

Is there something I'm missing?

Press jump.
When you are in the "exit" system, there should be an arrowed "next sector" button at the right border of select new system to jump window.

You probably just didn't see if for some reason, but it's added to tthe regular jump window.

Ok, I seei t now. I thought it was just some short cut feature for choosing your next destination.