For about half that amount, you could buy a mid-1980's Yamaha SBG 2000 or 3000. I own a 1984 SBG 1000. It doesn't have a sustain-enhancing brass block under the bridge like the higher models do.

I bought it new, after doing a one-on-one comparison with an LP Custom. At the time, the LP cost $1300. I bought the Yamaha (for $640), not because it was less money, but it because it was, and is, a better guitar! Fit and finish were perfect, it was set up well, right out of the box, and a lovely, plush lined, hard-shell case was included. I have since changed the pickups and modified the switchgear, but that was a matter of personal preference. I certainly didn't have to do so.

A check of Harmony Central writeups will show you that SG/SBG owners agree that Gibson guitars are more hype than performance. If you can find one, close your eyes and let your hands and ears make the assessment. If you still choose the LP, at least you have made an informed decision... and if everybody had identical tastes, there would only be one kind of guitar in the world. :)