Hm, I think cut and color are important. I felt MUCH more myself after I cut my hair and it was not (literally and psychologically) weighing me down.
That said, I don't style it. I run a brush through it in the morning and that's about it. I have forgotten to brush it on occasion and nobody can tell. I sleep on it wet and let it dry how it will. I don't think I've used my hair dryer (well, for hair at least - I have used it for DIY projects!) in the last year.
The thing about hair is that I'm not interested in it the way I'm interested in clothes. So I want it to look good but I want to spend minimal time thinking about it. I am happy sporting the exact same hairstyle every single day. Kind of like Steve Jobs and his black shirts.