I will second the recommendations for C. J. Cherryh's Company Wars books set in her Alliance-Union universe. Start with Downbelow Station - even though it's set near the end of the conflict, it sets the stage very well by giving background history in its preface/prologue. These books contain a hodgepodge of elements: space opera, hard sf, thriller, military sf, sociological, anthropological, economics, political, etc. Taken as a whole, they are definitely space opera and damn good.
And another big shout-out for Iain M. Banks' Culture series of novels - possibly the best space opera books ever written, certainly one of the most literary, even amongst luminaries like Dan Simmons, M. John Harrison and others. I could write on and on about the Culture as an introduction, but I won't. Just try starting with The Player of Games, the second published Culture novel. These novels aren't exactly a 'series' per se - each novel is completely independent and self-contained. Hardly any of the characters re-occur. TPoG is less action packed than some of the other Culture novels, but it's definitely an ideal starting point, despite its relatively slow first section. Banks essentially set the standard for the resurgence of modern space opera with the way he combined existing tropes in novel ways to create a very unique post-scarcity civilisation. Many of these features are now common in the space opera of other writers.
For a frenetic, action-packed, very fast-paced space opera from beginning to end, check out Scott Westerfeld's Succession duology. One of the most fun space operas I've ever read post-2000. Battles from the millimetre to relativistic scales, some politics and even a dash of romance. A little tech savvy, but not at all difficult to understand.
David Brin's Uplift books are also very, very good. Give them a go starting with Startide Rising and follow that up with The Uplift War.
Besides Banks, my other favourite space opera author is Alastair Reynolds, but he's much more dense with his prose, spends some time on very fascinating digressions and is much more concerned with keeping faith with science. I definitely think you should try him, but maybe he's not exactly what you might be looking for. His Revelation Space series of books are required reading, in my opinion, but maybe you should start with his independent novel House of Suns, which is considered one of his best by many.