Beck is mostly associated with one of 3 Les Pauls over his career. The first one appeared when he was in the Yardbirds, it's always seen with it's covers off showing double whites so it's a 59 or 60. It always had a single layer black pickguard in the beginning never a cream one.
... after a while it lost the pickguard and the switch-ring.
When Beck throws a tantrum and leaves the Yardbirds in the middle of their American tour he supposedly smashes this guitar up to some degree, however it's repaired and back in action for the Jeff Beck Group.
By now it's had all it's top finish stripped off.
Another tantrum and Beck smahes it up yet again, once again in the middle of an american tour probably destroying the neck this time. Luckily Rick Nielsen (of later Cheap Trick fame) is on hand to sell Jeff a considerably nicer flametop 59 burst, this is absolutely the guitar that's in the Beauty Of The Burst. Beck uses this till it is eventually stolen.
sometime around here Jeff gets back the first guitar. Going by the photo in the bacon book it got renecked with a new fingerboard, big headstock with flowerpot and script logo inlays and jeffs intials at the end of the fingerboard. the enterprising (but unnamed) luthier also made off with the double white Pafs that were in it. apparently Jeff never really liked the result and I've only seen a couple of photos of him using it (circa Rough & Ready) in this state, he still has it.
Lastly around BB&A he picked up the "Oxblood" (really very dark brown) 50's conversion that he is often pictured with, it came from Strings & Things who I think have some sort of blurb on their web page about it's history.