お早うございます、
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.
最
meansthe most
coupled with any other kanji that has a degree of measure you can get an idea of how it can be used.最小 = the minimum
最後 = the final
最初 = the first
etc. With 一番, by replacing the 一 (1) you can do三番 = third
五番 = fifth
and so forth.