Hi Angst of Parting,
Definitely Cordwainer Smith - his stories are awesome, and his themes resonate through pretty much all modern SF, and absolutely throughout Mindjammer. Banks's Culture novels too - although quite bizarrely I only started to read them *after* publishing the first edition Mindjammer book, as Chris Birch at Modiphius said, "hey, it's like Iain Banks's Culture, right?" - and I was like "Okay..."
I've read 4 or 5 of them now, and I'm struck by the similarities and differences - many themes are there, but also the *huge* difference is that the Commonality is very humanocentric.
Also I'd recommend Olaf Stapledon - Starmaker in particular, but also First and Last Men - and Dan Simmons' Hyperion and Peter Hamilton's Commonwealth Series (and even Night's Dawn). Also definitely give Jaine Fenn's Hidden Empire series a look - tons of cool ideas in there.
I'm reading Alaistair Reynold's Revelation Space for the first time at the mo, and finding some excellent ideas there, although it's a bit of a slog; and I have Neal Asher's "Agent Cormac" novels on my bedside pile after someone on the G+ community recommended them. Such a lot of great SF to read!
I also read loads of non-fiction pop science; Gardner's "Intelligent Universe" is worth a read just for its mind-bending scale and potential. And of course Kurzweil. Then tons of history - John Julius Norwich's Byzantium trilogy and Alain Peyrefitte's "Immobile Empire" are just awesome for getting into a Core Worlds mindset. ;-)