I agree with fulldistortion,pick your gauge and then check your intonation.I know you have a les paul but if you had a floating tremolo, a string gauge change would require an adjustment to the springs of the tremolo.
Yeah. I bought the guitar and a string broke pretty much right away.

I bought standard size (11s) because the guy at Long and Mcquade said, "Yeah this size will work fine" but I was getting buzz on my Low E. Carelessly, without thinking that I might be getting buzz from string gauge, I tried adjusting the height of my bridge on the low side, but nothing helped. I think in the process I screwed up my intonation. :/ So I'm going to bring it in and get it all reset.
.10s. It's the stock strings, and as an Epi LP owner (I have two) AND rhythm guitarist with little lead experience, I enjoy .10s. .9s are too skinny for me anywho.
-Epiphone Les Paul Standard Plus Top Lefty
-Epiphone Les Paul Special II Lefty, name's Sonny =)
-Danelectro CM-1 Metal Pedal
-Danelectro CC-1 Chorus Pedal

I've been playing since Summer '09
Pick a gauge and have it set up for that gage. If you want to keep your warrantee, use .10 since that's what is used stock. Otherwise, pick a gauge and go with it.
Current Rig:
Gibson Firebird Studio
Limited Edition Schecter 35th Anniversary C-1
Schecter Jeff Loomis Signature 7 FR
Ashdown Fallen Angel
Custom 7 Firebird from Ignition Custom Guitars (check them out)
ESP Phoenix
I came into this thread prepared to post what FullDistortion already posted.

TS, you gotta try the different gauges and see what you like.
I play lead parts in Standard tuning with .10s and my guitar has a longer scale length than the epi, but I have no problems.
ten heavy bottom period. loose enough ot easy bend and have tons of contol and feel, heavy enough so your not playing rubber band 9s in a short scale guitar, and a les paul chunk with .52 bottoms give punchier bass.