***rummages through the gray matter***
Didn't I read Starship Troopers and decide I didn't like it? Seems like I did a couple of year ago at thebeach.
"Starship Troopers" is never the book one should read to start Heinlein. His tendency to lecture comes out a bit too strong. If you don't already know and understand his style, it just doesn't work, there's not enough plot to hang the essays on. It's like "Atlas Shrugged". Only, well, readable.
"Moon is a Harsh Mistress" has some of the same tendencies. That's why a short story collection is probably the way to go. He doesn't have as much room to warm up and has to focus more on just the story.
Can't figure out what particular story to tell you to start with. I am awfully partial to "The Menace From Earth" but that's because I first read it when I was 16 and liked to think I was the heroine ;-) "The Long Watch" is pretty... gripping. I think it's in the "Man Who Sold the Moon" collection but I don't have the contents memorized.