At the risk of insulting some folks here, I don't buy into the widely parroted Gibson QC story - and that story isn't "recent". I don't see Gibson turning out clunkers at a higher number than any other mass produced brand. Gibson, it seems, is held to an impossibly high quality standard compared to other brands. Sure, they turn out clunkers, just as any other mass producer does.
The best way to avoid that is to play before you buy. Look the guitar over very well and be sure you're happy with it before you hand over the money...............................just like you should with every guitar, regardless of brand.
I own three flawless Gibsons that put a smile on my face every time I play them.
All of that said, there are a bunch of Les Paul models to choose from, with widely different feel, sound, and looks. Your best bet is to get out and play as many as you can. You'll know the right one when you play it. Tune out the internet noise and be your own judge.
Good luck on your quest.
Guitars: 2008 Gibson SG Classic, 2006 Gibson Les Paul Standard LE, 2002 Gibson SG Supreme, 2001 Gibson Les Paul Studio Plus, 1996 Les Paul Studio Gem, American Deluxe Double Fat Strat, Bluesville "Super" Strat Copy, MIK Fender "Limited Edition" Tele, JD Bluesville "Night Pilot", Yamaha AES 820, Steinberger Spirit GT Pro, Taylor 355CE, Ovation 1897 Adamas, Ovation CC057 Celebrity
Amps: Axe FX centered rack rig, Mesa 4x12 cab. Germino Club 40, Johnson JM150 Millennium, Johnson JM250 Millennium, Gibson Titan Medalist Frankenstein.
Effects: Tonebone Trimode, EH Holy Grail, Boss CH-1, Dunlop Crybaby Classic, Framptone Amp Switcher, THD Hot Plate, Yamaha AG Stomp Acoustic Processor, Boss BCB-60 Pedal Board.