Looking back, I quite like how the original show wrapped up.
While they overcame some big challenges and saw some crazy things, the crew of the Outlaw Star are still people with tangible, believable personalities and pursuits.

I've hypothesized as to the direction of an OLS sequel before.
Perhaps Suzuka and Aisha could have more "solo missions", or miniseries which revolve exclusively around them to give their characters more flesh. However, because Gene, Jim and Melfina are tied to the Outlaw Star we would need to be a bit more inventive in order to get character study-like series for them individually.

Not impossible by any stretch, though. Perhaps they want to upgrade the ship in some fashion, and due to its sophistication and connection to the Space Forces and Pirates, such a task is not so simple, so they would have to spend time on a planet or at a dock, where they end up getting separated as the result of some conspiracy to steal the ship. Then, during their mission to regroup, we have more individual character-themed episodes.
However, it would take some serious doing to push that into thirteen meaningful episodes.

So, as far as sequels go, I would just be happy to see these characters again, faithfully represented and not botched like many attempted sequels in media.

For prequels, I would definitely shoot for a Hilda miniseries. She plays a pivotal role in the show, but enjoys very little screen time.