Arduino + MOSFET + TLC5940

Hey, that did something

First, I tried a 10 k? resistor with a fading sketch, but with that the LEDs would never switch off.
With a 330 k? resistor, the fading goes from 80% to 100% (approx., could also be from 50% to 90% or so).
Unfortunately I can't find the right resistance to be able to make use of all 256 brightness values I send to the TLC.
With 1.32 M? for example I can change the brightness from 50 to 170, everything over 170 is off, everything under 50 is fully on.

Right now, I only have this one FET and I need to buy a couple of them so it might be easier to directly buy the right ones!?
Could this one (http://www.irf.com/product-info/datasheets/data/IRLZ34N.pdf) be suitable? (it is an n-channel FET, but I did not find any available p-channel FETs and when I want to switch the LEDs completely off, I have no problem with disconnecting the power supply)