I disagree 100%. A high quality guitar should be your no.1 priority. You can get better and better amps as you go along, but a poor guitar will retard your playing. Spend the money on the guitar, like you're thinking.
A Gibson Flying V is one of Gibsons really good deals. Some of the Marshall Music stores are now selling Gibsons and they ought to be able to sell you one for the price range you're looking at. Btw, the way to play them sitting is to put your thigh into the V ?.
I'm not a fan of LP Studios. I think the lack of binding kills the LP look. I'm also a luddite and don't trust Les Pauls that are lighter than Strats ? They sound good though, but they're not a very traditional LP.
My recommendation at that price range will probably always go to the Tokai LS92 - LS100. Clones of '50s Gibsons that easily match the quality and features of a R20,000+ Gibson LP. And they're even more vintage styled than those R24K Gibsons. Phenomenal guitars in that price range if you like '50s style Les Pauls. I have both a '80s Gibson LP and a high end (LS160) Tokai Les Paul, and although I love my Gibson, the Tokai is a lot more like a '50s Les Paul.
Here's my Tokai just to demonstrate that it's a clone of a '50s Les Paul, rather than a lookalike, like an Agile, for example:
edit: Thought I'd put in that the PRS SE range is very high quality for the money, as is the Ibanez Artcore range.