Since you are saying "I am the best" and that statement alone carries a bit of ego/arrogance/boast of confidence etc. I would think you'd want to use 俺, 私 sounds neutral/formal. And for the particle, you'd use が since you are pointing out that "I" am the best and none other.
For your second question, both mean relatively the same thing. Though, 一番 is more like, the best, the first (in a series of things or events that can be ranked). 最高 takes a meaning of "the most, the highest, the greatest."
So it just depends on what tone you want to set with your statement.
I hope that helps.