Not all CJ Cherryh books are the same. She writes in a few different styles.
If you want a fast starter, read
The Pride of Chanur. Short book. Then there's a trilogy after that and a final 5th book that happens a few years later. They're my favorite series among things she's written.
Of course THE "classic" Cherryh book is Hugo-winner
Downbelow Station, which is definitely a slow-starter. It's even got an infodump at the beginning, something I believe her editor wanted. None of her other books do the infodump thing, just going in media res. Her fantasy
Fortress in the Eye of Time is also a very slow starter; the first 100 pages won't give you any sort of idea what the rest of the series is like.
But anyway, the definition of "classic" in this thread is rather unclear.
Right now I'm reading Asimov's
The Gods Themselves. I haven't read it before, and I was almost to the end of the 2nd part before I realized one of the songs on one of my filk CDs is based on it. I was like, "whoa." It's the novel he wrote in his huge novel-writing gap years. Quite good so far.
We started reading Heinlein's big story collection
The Past Through Tomorrow, which has his whole future history timeline, including fantastic stories like The Man Who Sold the Moon. Definitely a book to read, good old hard sci-fi from the 30s/40s and a bit later. In bite-sized pieces! (Though some of the stories are pretty long.)
I just finished listening to
Jonathan Strange and Mr. Norrell on CD in the car. Just came out last year, but it's an instant classic. It reads like it was written in the middle of the 19th century, and it's set from about 1807-1816. Neil Gaiman called it the best speculative fiction book of the last 70 years, and it's certainly a contender for that title.