The first example is incorrect. The second and third examples are both correct. Which one you use is mostly a matter of preference, although a hundred appears more frequently than one hundred. There is also another form, an hundred, which was common in the past, but has mostly fallen out of use. See Google Ngram Viewer: a hundred, an hundred, one hundred:
One-to-one is used when you talk about transfer or communications. You may use one-to-one when you can identify a source and a destination. For eg., a one-to-one email is one sent from a single person to another, i.e., no ccs or bccs. In maths, a one-to-one mapping maps one element of a set to a unique element in a target set. One-on-one is the correct adjective in your example. See Free ...
"Which one is the best" is obviously a question format, so it makes sense that " which one the best is " should be the correct form. This is very good instinct, and you could even argue that the grammar is good, but at best it's unnatural.
It is possible that the singular/plural choice is not a purely syntactical matter, but partially depends on whether the speaker's focus is on one or on more. If it is expected that there will be more than one (and one is included just to cover all the possibilities), it is natural to use the plural.
Which is correct: "one or more is" or "one or more are"?
Which came first when saying numbers: "one hundred AND one" or "one ...
Some people say a dog=one, dogs=ones, the dog=the one=that, and the dogs=the ones=those. It's a rule of thumb, but what I found was that this is not always correct.
As @PeterShor points out, in this case "one" is the pronoun, and would never be numeric. Beyond that, as a general rule, spell out numbers 1-9, but for technical writing, it may be appropriate to always use the numeric version when you're referring to a numeral (as opposed to the pronoun example above).