I was planning to amplify to the required 10v dc using a simple op amp non-inverting circuit
You would be better off just using a transistor with a pull up to 10V.
My question is do I have to control this from a PWM port
You do if you want to control the brightness then you have to use PWM.
however it doesn't specify how big ?
About 10uF should do it.
best sensor to use for measuring humidity
Tricky ....... humidity is hard to measure accurately electronically and sensors tend to only be 10 - 20% accurate. Plus they age over a year or so and don't produce consistent readings.
I would use the wet & dry method with temperature sensors and a controllable fan to move the air over the wet one.