I first picked up science fiction when I read Heinlein's Tunnel in the Sky as a 14yo, but the following year, I was completely hooked when I found EE 'Doc' Smith's Skylark series. I found and devoured the Lensman series later on, and that completed my baptism.
I second the comments about Anne McCaffrey's Dragons of Pern series. Love 'em, and re-read them regularly; it's like visiting old friends.
Asimov's Robot series is also good stuff to feed young minds. There are a lot of good Asimov anthologies out there too, although probably a lot are out of print. Same for Heinlein.
I'd recommend some Poul Anderson, too, to introduce the concept of harder science fiction. Orion Shall Rise is a good one.
Finally, I can't leave a recommended reading list without mentioning Lois McMaster Bujold's Vorkosigan series. Wonderfully written space opera about the capers of a physically handicapped but brilliant military-minded dwarf; I love the squiggly-minded little man! And he has a great supporting cast of characters, too. :)
Whatever you decide, enjoy!