I won't post spoilers for those in the middle of the series, but I will make some general comments for those just thinking about starting the series.
1. Do it! If you love a great, sprawling, intense, who-dunnit-thriller-space-opera, this series is for you.
2. Anniversary Day is one, over-arching story told over multiple volumes...because its so /big/.
3. The saga includes favourites from the previous Retrieval Artist standalone novels, but they are part of a much larger cast of characters, all of whom have a vital part to play in the development of the story.
4. The alien cultures that trigger the whole 'retrieval artist/disappeared' phenomenon are very much a part of the story. But. This is still a story about humans, first and foremost. More importantly, it's a story about individual humans who have to cope with a universe in which human laws and human values often have to take a back seat to the laws and values of alien cultures.
5. Because the story is character driven, many of the underlying themes - such as the cloning of human beings - will make you think about what it actually means to be human, but there is nothing 'preachy' about these themes.
6. And finally, the over arching story is so very well written that despite its strangeness, you will lose yourself in it. For a little while, you will escape gravity and live among the stars. This is what science fiction is all about.
On a personal note, I've read every single one of the Retrieval Artist novels, and the Anniversary Day series is my favourite.