I'm a science fiction fan, and if I was going to recommend a series for anyone to read, it would have to be Ben Bova's "Grand Tour" series. Its something which captured my imagination completely. You don't really have to read in any particular order, but some books should be ordered because of references back and forth. I've found the books to be believable... that is, there arent any bug eyed monsters, or crazy aliens, or any of that stuff... its just about humanity spreading through the solar system, and how Bova thinks things will progress. All of them are on my read-again... and again... list. I started with "Mars" (incidentally, being made into a movie even as we type). And, he's still writing new material.
The list is here on his website.. I used it to try to keep in some kind of order of reading, but you wont find book synopses there, alas.
http://benbova.com/about/
Here's a Mars synopsis, from Amazon.
"To the harsh landscape of Sol's fourth planet travel thirteen astronauts, the best scientists from eleven nations, on a history-making voyage into the unknown. The international crew of the Mars mission have spent nine months in space, crossing 100 million kilometres, to reach the last great frontier. Their voyage is fraught with disputes, both personal and political, and their time on Mars limited to 'footprints and flags'; yet while there they will come face-to-face with the most incredible and shocking discovery of all."
Stephen Baxter is another favourite author whose Xeelee series caught me, but then I began reading his alternative histories (Destiny's Children series). The 2 book series that captured me most of all was Flood, followed by Ark. Again... believable (could it really happen? Maybe) The Xeelee was not, but was interesting nonetheless and I will read all of those again, as well.
Baxter also wrote (with Terry Pratchett) the Long Earth series, and he has collaborated with other authors as well.
Here's the link to his books list
http://www.stephen-baxter.com/books.html