^Well, the problem (one of the problems, IMHO) with planning to read Rama II is that it doesn't tell a complete story. The Gentry Lee sequels are the kind of "trilogy" that's actually just one really, really long book arbitrarily hacked into thirds. Neither of the first two volumes has anything I'd consider an ending. That was one of the things that frustrated me about them and made me give up after two volumes, because I read them when they first came out and it was annoying to have a book just suddenly stop with no sense of resolution and know I'd have to wait a year or two for it to pick up again. I guess it wouldn't be so bad now that you can get all three at once and read them back to back, but if you want a complete story, you'll need to commit to reading all three books. You can't just sample the first one and expect any kind of resolution or fulfillment.
I had the same problem with Timothy Zahn's Star Wars Thrawn Trilogy, and on that one as well I lost interest after the second volume. Thanks to those two reading experiences, I resolved that if I ever wrote a trilogy, each installment would tell a complete story in itself, or at the very least, I'd make sure the story logically divided into three distinct phases so that each volume had some degree of resolution. In fact, by strict definition, that's what a trilogy is: three distinct stories that are unified by a larger arc or theme. If it's just one story sliced into three pieces based only on length rather than content, that's not really a trilogy, just a three-volume novel.