According to Silverberg's introduction to Vol 1, the series was created in early days of the founding of SFWA. While Nebula Awards recognize recent stories each year, the idea of Hall of Fame series was to recognize stories before the founding of Nebula Award - sort of one time equivalent of Retro Hugo.
Process of story selection was similar to that of Nebula Awards; so it's convenient to look at the series as Nebula Awards for stories written before official annual Nebulas.
Voting was in two categories - stories up to 15,000 words (short story & novelette), & those larger in size (novelette, novella, novel). Former went into Volume 1 (1970), edited by Robert Silverberg; later into Volume 2 (1973) edited by Ben Bova. Vol 2 is in turn split into 2 books - 2A & 2B because of too much material. In the entire set, there is only one novel (in Vol 2A); everything else is short fiction.
And, with very few exceptions, the selections are from a period of about 30 years preceding Nebulas. A total of 26 stories in Vol 1, & 11 each in Vol 2A & 2B. Means less than 2 stories for each year - mostly in short fiction category.
According to Ben Bova's introduction to Vol 2A, there were two more stories of larger than 15,000 words that qualified but "were unavailable for this anthology": Walter M Miller, Jr's "A Canticle for Leibowitz", & Ray Bradbury's "The Fireman". Former is now more readily available in an edited & renamed avatar - "Fiat Homo", the first of the 3 stories included in the fix-up novel also called "A Canticle for Leibowitz". According to Wikipedia, Bradbury's novella "The Fireman" was itself an expansion of an earlier short story "Bright Phoenix"; novella was later expanded into the much better known novel "Fahrenheit 451".
Over the years, there seem to have been extensions - sort of milking the "Hall of Fame" brand as a franchise. So there have been Vol 3 (1981) edited by Arthur Clarke & Geo W Proctor, & Vol 4 (1986) edited by Terry Carr - both containing stories that have won normal Nebulas.
Note: If you landed here looking for ToCs of these two volumes, here are external links to them: Vol III & Vol IV.
There are also two Ben Bova volumes from 1975 - "Science Fiction Hall of Fame: The Novellas" - Book 1 & Book 2. I don't really know their rationale. Their contents seem to be subsets of Vol 2A & 2B.
For the moment, I'm only interested in original pre-Nebula content. Hence only 3 links below; links are to detailed reviews of the books.
The Series (3 books).
- Robert Silverberg (Ed)'s "The Science Fiction Hall of Fame: Volume One, 1929-1964" (1970): 26 stories, all read.
- Ben Bova (Ed)'s "The Science Fiction Hall of Fame: Volume Two A" (1973): 11 stories, all read.
- Ben Bova (Ed)'s "The Science Fiction Hall of Fame: Volume Two B" (1973): 11 stories, few read.