#1
I own a 2012 Les Paul Studio with stock pickups and I'm looking to upgrade them. The tone I generally try to use is a warm clean sound.

Any suggestions?
#2
Duncan Alnico II Pros are a popular choice for that sort of thing. Depending on your budget you could get some serious custom/boutique pickups but that gets expensive in a hurry.
#3
I'd start with theses:

RailHammer HyperVintage:
http://www.railhammer.com/hypervintage_neck.html
http://www.railhammer.com/hypervintage_bridge.html

Tesla OPUS-1 and OPUS-4
http://www.teslapickups.com/?products=opus-1
http://www.teslapickups.com/?products=opus-4

Vintage Vibe HS540 or Blade
http://vintagevibeguitars.com/windows/H540AlOpenWin.html
http://vintagevibeguitars.com/windows/hum_bladeWin.html

Besides those pickups, the makers have others that may also fit the bill. And if those don't do it for you, check out The Creamery, Rio Grande, Lollar, Lace, TV Jones and Bareknuckle (in no particular order).
Sturgeon's 2nd Law, a.k.a. Sturgeon's Revelation: “Ninety percent of everything is crap.”

Why, yes, I am a lawyer- thanks for asking!

Log off and play yer guitar!

Strap on, tune up, rock out!
#4
Warm clean isn't really much to work with. Honestly, you can get a subjective Warm Clean from any high end pickup you buy as long as it compliments your playing in that way. I'd listen to demos and try to identify a pickup that you think would compliment your style.
#5
Personally, I'm a fan of Seymour Duncan pickups- Their Vintage Output humbuckers would probably fit what you're looking for.
http://www.seymourduncan.com/products/electric/humbucker/vintage-output/

Based on what I've used, I'd recommend these:
http://www.seymourduncan.com/products/electric/humbucker/vintage-output/59_model_sh1_an/

You can find plenty of demos of different pickups on manufacturer websites, I'd listen around a bit and find what suits you, as Joseph said.
http://www.seymourduncan.com/support/audio-samples/humbuckers_and/ is a link to some Seymour Duncan humbucker sounds.
#6
I'm loving the cleans on my Duncan SH18 set (Whole Lotta Humbucker) they are quite similar to the Alinco II's but its a rough cast Alnico 5 magnet so its a bit hotter and they really did boost the output of the high B and E strings. I noticed with the stock 57 Classic's from Gibson these two strings were noticeably quieter in comparison to the rest this is not the case with the SH18 set. They are aimed at the Zeppelin fans as they are a recreation of Mr. Page's pickups but they certainly fit the bill for any of that old vintage London sounds. I'm a sucker for Alnico pickups though, this weekend I am going to toss the 57s into my Explorer in place of the ceramic pickups in it.
2011 Gibson Honeyburst LP Trad. w/ SD Whole Lotta Humbuckers
2014 Gibson Ocean Water Standard Plus
Marshall Haze 15W Head/Cab
Hughes & Kettner Tubemeister 5