"Cat" was also my first Heinlein book (well, aside from a couple of juveniles) and I loved it but I was SOOO lost. Reading the other books really makes you appreciate it more. But as I said, no ending! You have to wait to "Sunset" before you find out what happened.
Sorry to hear you didn't like the Starship Troopers movie, but the novel is quite different, and definitely worth a read.