You have to bear in mind, if I was only allowed one guitar, it would have to be a strat... (alder body, rosewood board, vintage radius, standard trem with all five springs installed, but tightened down so it doesn't move, single coils, 5-way switch, tone re-wired as a single master, other knob left as a dummy)
But bearing all that in mind, I'm with sgmypod, I love the idea of les pauls. The Gary Rossington looks stunning, as did the second one Will posted. And I had a peep in Billy Gibbons's book the other day, there's a close-up of Pearly Gates in there that, well... swoon...
I'm also with HEAVIER THAN HELL. I've tried a few times to like PRSs - they are obviously class, but they just don't do anything for me when I play them. I've not laid hands on a Mira, but a while back I tried a few others, followed by two Gibson LPs. The PRSs and one of the Gibsons all had a similar effect on me - classy but not speaking to me (the PRSs seemed better made, btw). The other LP, on the other hand, was gorgeous to touch, play, etc... I was sorely tempted, but I don't regret not buying it - it was £1400, and too much as far as I was concerned (I got a Love Rock a month or two later that feels almost as good - not quite - for a lot less than half that).
I wouldn't pay big money for a strat either, by the way - I know you can get a killer (with Fender on the headstock), brand new, for around £550, then add some BKPs, who needs to pay more? :D