I have got a new Gibson Les paul 1960's classic re-issue which is amaizing!!!!

I am wondering what strings I should use.



or 13.?

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more info needed. What style of music do you play? what will the guitar's tuning be set up? as and what would the other gauges be for the rest of the stings?
The answer is and will always be whichever one you prefer. But yea we probably just need to know about the lowest you will go in tuning to determine that string gauge, not too sure how the style of music will affect what string gauge you use but meh.
In terms of tone - I'd go for the heaviest possible for your style of music.

Lots of bending or really fast shredding might be difficult on 12s or above unless you've got the action set low with appropriate neck relief.

Lighter strings = easier to play but you'll sacrifice some tone.
For general playing you could try 11s. Other than that provide more info on your style and what music you like to be more helpfull =D
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The guitar probably came with 10's. If you step up a gauge or two it's likely you'll get some binding in the nut, the truss rod will most likely need to be adjusted to compensate for the greater string tension, and of course intonation will need to be adjusted. If you're comfortable doing these things fine otherwise be prepared to pay 50 -70 for a decent setup.
Moving on.....
Thickest possible for best tone really unless you're shredding in which case it would be hard on 12s or 13s. I like 12s in standard (possibly half a step down, it's been ages since i checked ) on one of my guitars.

Then again i'm a really slow player xD