Is there a best order for running the SOS adventures (including those included in the main rulebook and the Quick Start guide)?

Small Mercy -> Heir to Darkness form an obvious arc, and then Eviction Notice -> Dreams and Dust form something of another arc.

Personally, I would recommend Small Mercy -> Heir to Darkness -> Eviction Notice -> Dreams and Dust, as that order lends itself fairly naturally to PC growing in terms of importance in the game world. It starts the PCs out in the Belt for the first two adventures, then brings them to Mars for the last two.

Ghost Ship (from the core) can easily be inserted as an interlude before Small Mercy, between Small Mercy/Heir to Darkness or between Heir to Darkness/Eviction Notice. It's rather short compared to the other adventures, and doesn't really touch on the same plot threads, so it's easily moved around. It's probably better to put it somewhere in the first half of the sequence, though. In my opinion, it's the least interesting of the adventures in terms of plot, but it works pretty well as “training wheels,” getting used to the system, in particular with players learning how combat works and how lethal it can be.

Memories (from the Quick-Start), honestly, is difficult to fit into the sequence, since it's written for the specific characters that come with the scenario. It can be ran anytime as a side story, and does serve to foreshadow the tensions between Unitech and the Stillwater community that comes into play in Dreams and Dust. It can also work as training wheels for learning the system, because if the players underestimate the lethality and die horrible, bloody deaths, it really only affects them for that one session (since the characters are only for that session).

Actually, if you want an excuse for your players to have a ship early on, running Memories first to get used to the system, then having the players make their normal characters, and then having those characters “salvage” the ship from Memories (since there's likely to be only one or two survivors from that scenario), could be an interesting narrative link.

So - short answer - if I had to put all six adventures in sequence, they'd go something like this:

Memories -> Character Creation -> Small Mercy -> Ghost Ship -> Heir to Darkness -> Eviction Notice -> Dreams and Dust.

Thanks for the excellent advice. This really helps me with my planning - I'm hoping to start running a campaign early next year.