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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.
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:
How one and one's is different from other indefinite pronouns The possessive of one (one's) is formed the same way as the possessive of other indefinite pronouns, such as someone (someone's), but it is used a bit differently. For most people, one is consistently used with the possessive form one's.