Oddly, I read Manly Wade Wellman's mash-up of Sherlock Holmes and the War of the Worlds before I read the H.G. Wells original. Kinda colored my reading of it, though not in a bad way. :)
I didn't grab Heinlein until college, where I fell in love with the Past History story collection.
One I enjoyed that hasn't been mentioned was Diana Wynn Jones, with Archer's Goons and Howl's Moving Castle. I was excited when Miyazaki made it into a film, despite the changes in focus and story.
I barely read at all until i had a Sci-Fi english class in High School. We read Fahrenheit 451, and i was hooked, and read any Bradbury I could get my hands on. We also read Jurassic Park, and Childhoods End, which I LOVE.
I read a lot of sci fi growing up, but the one that sticks out as having the biggest impact on my life in high school was Neuromancer. After finishing it, I was a Gibson fan for life. I'd read Asimov, Heinlein, Clark, and similar era writers, but this was 100% new and came out of nowhere. Cyberpunk is mostly dead these days (I believe) but I really believed it prepped me (and a lot of us) for the Internet-based lifestyle so many of us swim in these days. I'm still waiting on my immersive Matrix-style navigation of the Internet.
Cyberpunk was at the cutting edge of what virtual reality/cyber reality could do. It's hard to write good speculative stuff in that direction since the technology moves so fast now! Still, Elizabeth Bear has an excellent series about a soldier that's basically half-cyber technology that might be close to what you're looking for.
When I was about eight years old, I discovered that my dad used to keep the books he was reading by his bed side table. In amongst the novels that he got from the public library were these paper backs called "IF", "Analog" and "Galaxy". They were packed full of short stories that I could read, and if I couldn't understand the words, he would tell me to go look them up in our copy of the Oxford dictionary.
Years later, I discovered that he had two subscriptions for these magazines. One came home, and he used to leave them for me to requisition. The other went to his workplace, so he could read them during his lunch break, and in the commute to and from home.
He got me reading Arthur C Clarke, Heinlein, and E. E. 'Doc' Smith. From there I ventured into reading Jack Vance, and Larry Niven. Then I left home, William Gibson and Bruce Stirling kicked in, and the genre changed for me. Dystopia suited me in my early twenties...
For fantasy, I read all the Robert E. Howard Conan books, then started playing DnD, and subsequently read Michael Moorcock's Elric series. I still think Elric is one of the coolest "heroes" out there. For Sci Fi, I started with the Dune saga.
Ender's Game (although that's since been spoiled for me by the author), lots of the classic stuff--Asimov's robot stories being the big one, and then anything else I could get my hands on... I think the first sci fi book I ever read was Frog and Toad in Space
Only one person mentioned Heinlein, but my first was "Stranger in a Strange Land". It was read as part of an English class and the teacher and I became fast book sharers after that.
Oddly, that's the one Heinlein I don't like.
And as I'm watching the Hunger Games take off, I can't help thinking that the premise reminds me of John Christopher's Tripods trilogy. Not the same, but the part about youngsters being co-opted and taken over is very similar.