Star Dragon and the Uplift novels a good start, actually
Star Dragon because of its depiction of a gengineering heavy civilization, the Uplift novels because they take place in a setting that is very old and complex.
I second Selden's recommendation of the two books by Vinge.
Beyond that...
Ian Banks' Culture universe is counted as one of the inspirations for OA (although it doesn't aim to be a hard science setting). I've even seen it said that OA might be thought of as the spiritual successor to the Culture since Banks passed away a few years ago. A nice compliment and a high standard to meet.
Anyway, my two favorite Culture books, which also do a good job of encapsulating the setting and its main concepts are
Excession and
Look to Windward. There are a number of other Culture books, but they tend to deal with issues of politics, social structure, relationships, and other more abstract issues and take place more outside the Culture than in it.
Another good Banks book that depicts a setting that feels something like OA is
The Algebraist.
The
Revelation Space series of books by Alistair Reynolds is also considered an inspiration for OA. The series is fairly massive and (tbh) a bit depressing before it's done. But a good read if you get into it.
For more of a space opera/derring do vibe, the
Human Polity novels by Neal Asher are highly recommended. Not hard science by any means, but fun if you like big explosions, major gun fights, and some pretty interesting adventures all around.
Diaspora by Greg Egan (currently being discussed on the forum actually), is a good exploration of life as an uploaded entity living in virtual reality.
Implied Spaces by Walter Jon Williams is a nice read.
The
Mars trilogy by Kim Stanley Robinson is set during the terraforming of Mars. It's a good series, but IMO the author practically makes you feel as if you're living through every year of the multi-century project of making Mars habitable. Whether you consider that a plus or a minus probably depends on the reader.
A few older works (but worth the read, if you can find them), would be The Hyperion Cantos (
Hyperion and
The Fall of Hyperion) by Dan Simmons and
Vacuum Flowers by Michael Swanwick.
In terms of getting a sort of 'Cliff's Notes' version of OA, I'd actually recommend the write up on us on the TV Tropes wiki. While it's not what I would consider 100% accurate, they do an overall very good job of summarizing the major setting elements in a fun and approachable way (although be warned, the site is something that can result in hours of checking out the tropes assigned to different books, movies, and online settings).
If you're looking for more background information about the scientific and technological elements of the setting, we can certainly provide those as well.
EDIT:
Another I just thought of:
Acclerando and
Glass House, both by Charles Stross - both highly recommended.
Hope this helps,
Todd