#1
I was thinking about buying the fender American vintage series 64 tele. The only thing that I'm worried about is not getting a low action. Jimmy Page is my biggest influence and I know he bent the strings and played extremely fast on his 59 tele. I actually prefer his tele sound over the lp. Any way does anybody know the lowest possible action without buzzing.
#2
My tele has pretty low action. Go try a few out and see what is best for you.
2002 PRS CE22
2013 G&L ASAT Deluxe
2009 Epiphone G-400 (SH-4)
Marshall JCM2000 DSL100
Krank 1980 Jr 20watt
Krank Rev 4x12 (eminence V12)
GFS Greenie/Digitech Bad Monkey
Morley Bad Horsie 2
MXR Smart Gate
#3
It varies by guitar, there's no universal lowest possible action.
Any halfway decent guitar with a good setup should have the ability to be set up basically as low as any normal person might want without buzzing. If you decide you need something super low you might need extra fret treatment and truss rod adjustments.

Since you're not Jimmy Page, not a ton of this matters. He also used .08s, which very few people find comfortable or playable. Don't get his setup, get one that works for you. Super low action isn't going to make you play like him (well, it might make you sloppier ... )
#4
There's a good point there, I got a Firebird Studio because I really wanted to get a Dave Grohl guitar. Unfortunately, not one single bit of that guitar was right for me, it was uncomfortable, heavy, my arm didn't sit right. The damn thing almost killed guitar playing for me altogether as it was my first proper guitar. Worst came to worst when I played an RG at a second hand store a couple of months later and it was all too right, and not even a Dave Grohl guitar. :S

Moral of the story, make sure the guitar is right for you, not for your idol.