Semantic Versioning is pretty much de facto nowadays.
I'm "missing" several minor versions, how do you guys handle that situation?
You're not missing versions. It's perfectly acceptable to… (see next answer)
Which is a good starting version number
Depends if people are using your code in production. If it's already used in production jump straight to v1.0.0. But since you said your code is alpha, beta, or rc (release candidate) quality but you're planning to move to production quickly consider starting with v1.0.0-[alpha].N where [alpha] is the software grade and N is a build number or other enumerable value.
Is it ok to make numbers above 10? like v1.25 or v2.2.30?
That's the idea. Lexicographical sorting may not work but that's okay.
