Is blues, jazz country, or rock the best style to learn as far as improv skill and technuque. I want to improve but dont know what to go with.
I'd say jazz would come first as far as improvisation and skill goes. Followed then by blues and country. Rock can go almost anywhere depending on what you're playing (eg: are you playing Phish or are you playing Metallica...)
i'd have to say blues for improv, then jazz, then country. jazz is a lot more improvisation but its a bit harder to apply to your primary style, which i'm assuming is rock. jazz will definitely open your eyes up and give you a new perspective on things.
"When the power of love overcomes the love of power the world will know peace."
- Jimi Hendrix
In order of learning, I'd go blues, country, and jazz.

I'd say that if you can do jazz improvisation proficiently, you have incorporated all the theoretical knowledge and physical skills required to play any of those genres.
He who joyfully marches to music in rank and file has already earned my contempt.
He has been given a large brain by mistake, since for him the spinal cord would fully suffice.

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Do what you feel like I started with blues then went to jazz and country.
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jazz is hard without having played some blues before, because though some may disagree their is some blues theory at the heart of jazz. Go practise the blues, it'll help with any other styles you play, and then if you want to follow on play some jazz. Its suprising who are fully trained jazz musicians, like Sepultura are. If you can jazz solo then you can solo like a madman .