The very best value for a Les Paul style guitar under $1K is to go pickup a used Gibson Les Paul Studio. You can find them anywhere from $500 to $700 in great condition (usually), and you'll have have a couple hundred bucks left over to swap out pickups, swap out hardware, or even repaint it using the colors you want.
I like some of the other LP styled guitars out there, but there's always a shortfall with them. For example, I really like the ESP Eclipses, but they are thinner than actual Gibsons, and the ESPs never sounded as resonant as an actual Gibson Les Paul.
If (for some reason), you're of the mindset to buy somebody other than a Studio, I'd have to advise you to spend some time with the Epi Les Pauls. They're great playing guitars that can go toe-to-toe with any other foreign made guitar line (LTD, Dean, Jackson, Ibanez, ect.), and since they can actually build a Les Paul to spec (except for multi-piece bodies and dat headstock), nowadays I'd prefer an Epi LP over any other "middle line" LP copy.
With that said; with your budget, I wouldn't even consider anything else...I'd buy a used Gibson Les Paul Studio and be thrilled. I'm of thr mindset that a budget guitar by a top manufacturer is better than the best guitar possible from a "middle line" manufacturer. I suppose it's similar to advice on real estate...always buy the cheapest house in the nicest neighborhood rather than the most expensive house in a cheaper neighborhood. You'll get more from your investment too! A Gibson has a two or three piece back, made of higher quality wood, with nitro paint, and better playability. There's always a plethora of Studios on the use market; so go pick your favorite color!