A friend read a bunch of Heinlein quotes I posted to a Listserv e-mail list. He was too young to know Heinlein, but as a libertarian, he found the quotes interesting. He asked for some book recommendations. When I was done writing, I realized I had a blog post:
I'd start with The Moon is a Harsh Mistress.
Other great stand-alone novels:
Podkayne of Mars
The Rolling Stones
Stranger in a Strange Land
Then there are a whole series of interlocking short stories and novels collectively referred to as Heinlein's "Future History".
If you can find a collection of the short stories before you read the novels, the novels will make more sense. The best collection is called "The Past Through Tomorrow". As a bonus, the foreword includes a timeline of Heinlein's Future History.
After the short stories, the series of Future History novels are awesome.
They all feature a long-lived fellow called Lazarus Long and his kin.
Methuselah's Children and
Time Enough for Love are my favorites.
After that, you read more of the adult novels he wrote after 1963 or you read all of the books he wrote for a "juvenile" audience and marvel at the subversive stuff he got past a blue-nosed editor whose only care in the world was selling books to libraries. Or you mix them up.
For a laugh, after you've read any two or three things, look over "Grumbles From the Grave". It's the book of unmailed correspondence he'd always threatened to have his widow publish after his death and it's hilarious.
Beware of the desecration of his literary legacy she committed thereafter. She had alternative versions of a number of books republished, restoring 10s of thousands of words his editor cut out.
In most cases, his editor was right. What she's permitted to be done to Stranger in a Strange Land is especially distressing. It turns a damn near perfect science fiction novel into a book so fat and thick, its essence is smothered.
Not that I feel strongly about it or anything.
Thanks for asking. Heinlein is one of my favorite topics.