As @Rodders says the Banks Culture books are not really a series but simply stories set in the same universe. There are one or two books where a character from a previous books appears where reading them in order helps but it is my no means necessary each book does stand on its own. Which is actually one of the joys of this 'series.' The Asher, Hamilton and Reynolds do tend towards linked series. though Reynolds has done more stand alone books and thinking about it another Reynolds book that would, I think, perfectly fit your spec is Pushing Ice.so here is my list:
House of Suns - Alastair Reynolds
Children of Time - Adrian Tchaikovsky
The Quantum Thief - Hannu Rajaniemi . Should i get all three boks? Sequels are even better rated than first one.
Exultant - Stephen Baxter
The Dragon Never Sleeps - Glen Cook
A Fire Upon the Deep / A Deepness in the Sky - Vernor Vinge
Bolos 1 Honor of the Regiment - not sure about this one, super-tank sounds...dummy... and hard to imagine space exploration there..., but reviews are good... have to think about it
The Praxis - Walter Jon Williams - Its a trilogy, but looks very good. Is it necessary to read all books, or can i try just first one.. does it have finished plot? I suppose it does not, since its trilogy
Would like to read something from Iain M. Banks. But i'm afraid of series, i know its almost neccesary for some epic story, but thats it... i'm always too curious how story goes on, but what if i don't like it, i would have a great dilemma . Also quality of books can vary, for example I loved first Space oddyssey, second was OK, third was bad, and i just found out there is even fourth part which i 've never read (please don't stone me ). Maybe i should try sugested The Algebraist, but i wasn't convinced much by desctiption and reviews about that one. Well and same concerns goes to Neal Asher Polity series.
Re Bolos, I've not read them myself, and whilst I believe they're not too pulpy I do believe they are very much heroic military SF that I don't think really fits your epic space exploration themes too well.