1. Shy girls are very cute and sexy, Im always attracted to shy girls, shame there's not many about.
2. I used to be a bit of a shy guy (I still am quiet, although not shy) the way I became less shy is through doing what I love. I enjoy filming and currently a student trying to become a cameraman. Over the last 3 years I've had to do a lot of work experience, talking to different people, phoning, negotiation, leading etc. as a result my confidence as increased loads. I'm not over confident, and still am quieter than most people but I have no problem communicating. It was hard at first but my passion for my chosen career was enough to make me want to do it.
If there's something you love doing then I recommend that you focus on that and get good at it. The confidence of knowing what your doing in that will spread over to your general communicating skills and you feel a lot less shy.
3. Hard to tell what's best, short term an out going guy might be best, I had an outgoing girlfriend 3 years ago and going out with her probably improved my confidence as well. We stayed together for a year but problem is our interests are different. The problem after a while when going out with an outgoing person is there constant need to do things and see people, clubbing etc. gets annoying for the shyer person and visa versa. Going out with a shy guy may seem awkward at first but at least once it gets going then you have someone who you are similar to.
Also remember the world isnt black and white, there are shades of grey. What about someone who is neither shy or outgoing (like myself lol) That way they will help build your confidence but still have many simulates to increase the chance of the relationship being successful.
Good luck I hope you find someone who is the perfect balance of bringing out your confidence yet being similar enough to have a good relationship with.
Was shy myself