As the title suggests I have a thousand bucks, 1200 at the most. I am buying an amp as currently I have an old bass amp with a distortion pedal and a crappy guitar that was second hand, and is falling apart.

I play a lot of stuff. Zeppelin, Pearl Jam, thrash metal, heavier rock in general but also in need of a clean sound.

And what kind of guitar neck is the best for someone with smaller hands to play standing up.
I'd go for a Les Paul or maybe an SG for the sound's you're looking for. Maybe even a strat or a Schecter.
Celtic FootballClub1888
You'll have to try them out yourself. You may never know, you actually might like the feel of thicker necks more than smaller necks; ibanez necks.

You can look some type of les paul type guitar. I suggest looking into etlists, high end epiphones. Also, you should look into the higher end LTD guitars. They have seymour duncans in em' which are supposed to be quite versatile (JB and 59' in the neck I suppose...)

For the amp, I suggest looking into the cube.
Co-Founder of the Orange Revolution Club

-Esp/Ltd Ec-1000 w/ BKP Mules
-2-channel Titan
-Oversized Bogner 2x12 Cabinet
-Fulltone OCD
-RMC Picture Wah
-T.C. Electronic Nova Delay
-Larrivee D-03R