This is a very tough decision! And honestly, it resolves into Ibanez RG or most superstrats, really... I mean, you get everything - humbuckers, single-coil, whammy bar, neck accesibility.
If I have to choose an "iconic rock'n'roll guitar" - I'd go with Les Paul. Look - definetely Les Paul (well, with maple arch-top, to be precise). I have 2 LP's and barely use them, but they're just lovely to look at. Sound... well, LP too. edit: also, fixed bridge. Cool to play bends and other notes along with it, without going flat on other strings... not everybody needs tremolo, right?
Strat gets a whammy bar (at least some version of it... probably out-of-tune'y) and better accesibility from me. Also, it has a different, not worse by any stretch of the imagination, but sound for some other applications, definetely. So I'd vote for LP, but it's not really fair for the Strat side.
Now, the question is about which one "to buy", so I would recommend to buy a Strat, kind of illogically.
If a person will be able to put a bridge humbucker in there at some point, he'll get most of it...