I am interested in biking [and always has been] and I want to start biking lot more for fun. It's been long time since I biked when I was in high school and I lost touch. At this point of time, my fitness is terrible and please don't ask about my stamina. I want to fix that by biking to my office which is close to 8 miles from my home. That's a long distance for me to start covering from the day one so I am planning to take it in phases. First, I want to start biking to nearest public transit [a mile] and keep increasing from there. I need some guidance so that I don't cause more trouble than good to myself.

1. What is a reasonably priced bike that I can buy [first/second hand] that can make it easy for me to bike? I want to be able to bike on that in trails or parks as well so I am thinking of a mountain bike.
2. How much distance should I start biking on day one and how fast should I increase that distance so that I can bike to my office without using any public transit?
3. What sort of care should be taken to ride in cold weather [-1 C] and during night time?
4. What other suggestions would you like to give a new biker?

Thanks for taking time to read and respond!