I first picked up the original printing of the first volume of this anthology when I was a small child, around ten years old, and the first story in it ("A Martian Oddyssey") was so good that I put the book back down and didn't read the rest of it for another year because I was afraid none of the other stories in there could possibly be as good.
The second two volumes took me years to track down; II B I managed to find in a sale of discards from my school library; II A I didn't find at all until Amazon came along.
The conceit of this series is that the Science Fiction Writers of America picked the best short stories, novellas, and novels from before the Nebula Awards were commenced in 1965, and published them as a hall-of-fame anthology. Volume 1 collected the short stories and volume II (A and B) collected the novellas -- essentially, one stop volumes of all the "Nebula Emeritus" books, the sci-fi that professional SF writers of the sixties felt had most influenced and impacted them up to that point.
As such, this series is perfect for two groups of people: people who are completely ignorant of sci fi, and people who want to gain a better critical understanding of sci fi and its history as a genre. You can't find a better starting place, because these are the stories that the great modern SF writers started on, so by reading these, you'll understand more about what modern writers are doing, and you'll have the opportunity to experience the tropes first hand, from the stories that coined them, not in later knockoffs.
This particular volume has some really great stories in it, with a great deal of emotional impact. "The Martian Way" by Isaac Asimov is a great space yarn; "Earthman, Come Home" is an absolute classic; "The Machine Stops" has been amazingly influential (probably best seen lately in the movie WALL-E from Pixar) and "The Moon Moth" is unforgettably charming.
Probably the best benefit of these volumes is that they'll give you a general familiarity with the big names of Golden Age SF, so that you'll know who you like and don't and whose works you want to find more of. If I'd never read this volume, I don't know if (for example) I'd have ever read anything else by Jack Vance, and that would've been an absolute shame.
This volume contains:
"The Martian Way" by Isaac Asimov
"Earthman, Come Home" by James Blish
"Rogue Moon" by Algis Budrys
"The Spectre General" by Theodore Cogswell
"The Machine Stops" by E.M. Forster
"The Midas Plague" by Frederik Pohl
"The Witches of Karres" by James H. Schmitz
"E for Effort" by T.L. Sherred
"In Hiding" by Wilmar H. Shiras
"The Big Front Yard" by Clifford D. Simak
"The Moon Moth" by Jack Vance.