To anyone who has knowledge on this, I would add to the question by expanding it a bit.

Who and why did have the say on who are the presidents (apart from Hamilton, of course) represented on the dollar bills? Are there certain reasons why the person is represented on a certain bill?

I'll give a brief answer but I don't have a source to hand so it might be deleted and I wouldn't object if it is. The denominations 1,5,10,20, 50 and 100 are simply inline with international practice. There is no special reason the US decided on that break up.

Why the coin is 25 (which is indeed out of step) is because the US mint was influenced by the Spainish milled dollar. This was a silver dollar that was extremely common in the new world all the way from the discovery of the continent to the US coinage act of 1857 (which removed its status as legal tender in the US). As the currency was made of actual silver it's value was not based on the numbers printed on it, rather its value was based on the silver content. Given that this was the case the practice at the time was if you wanted to buy something that cost half a spainish dollar you would simply break the coin (or cut it I'm not exactly sure how it was done) in half. If something cost a quarter of a dollar you'd break it into quarters. You could even break those quarters in half to form 1/8th dollars. It's harder to break somehtin into 5th's as you would have to do to form 20 cent values. Thus the US decided to continue on with quarters. They also had half dollar coins.