You are right that your last sentence is good grammatically.
I want to help people, the more the better.
The comma in that sentence is acceptable, so would be a colon. The second, subordinate, clause is an idiomatic expression. The form of this idiom is always "The [X] the better", where [X] is a comparative adjective. A native speaker/writer might even use the expression as a sentence on it's own in some contexts, for added emphasis, perhaps with a comma. For example:
I crave grammar questions. The more, the better!
However, there are various problems with your examples 1. and 2. Say them and you'll be understood, but you'll sound like a non-fluent learner.
"... to more people the better." is just wrong - it's not a known English idiom. "... to the more people the better" is good. I wouldn't be surprised to hear it from an educated native speaker, but it sounds like a specifically British middle/upper class phrasing to me. A more international usage would be...
I want to make something useful to people: the more the better.
For top marks, though, you should use...
I want to make something useful to people, the more the merrier.
... this is because if you use better, it's not completely clear that you mean more people (finding it useful) is better, rather than more usefulness being better! "The more the merrier" is a common idiom used to say that a bigger group of people is desirable.
... Gosh, what a long answer already to a short question! :)