Outlaw Star

Gene Starwind and his partner Jim Hawking run a small business on the backwater planet of Centinel 3. But all that changes the day that Hilda hires them for a bodyguard job. Now, thrust into a mystery they don't fully understand, they're on the run from the cops, the pirates, an angry alien, and a mysterious assassin. But they've got one thing going in their favor - they have the galaxy's most advanced ship, the Outlaw Star.
Gene Starwind dreams of life as an Outlaw, and fate smiles on him as he seems to suddenly wind up with a great job. But as things go awry, and he finds himself the new owner of the fastest, most technologically advanced space ship in the galaxy. Unfortunately, it's stolen and the owners want it back... Along with his partner Jim and the lovely Melfina, Gene must fight his way across the galaxy battling pirates, aliens, and assassins as he attempts to discover the secrets of the Outlaw Star.

[Summary of Outlaw Star TV series, taken from ANN; there are significant differences between the anime and manga plots.]

Note: Chapters 18-21 were never released in volume form, and only through magazine serialization. As of January 1999 the manga has been on an indefinite hiatus with no update on when it will be continued.