I think this is what you're trying to say:
Have you ever known people who could spread their enthusiasm? They are the kind of people who inspire me.
A few notes about my edit:
1) Remove the "For me," part from the beginning. You're already personalizing this remark when you say "who inspire me" at the end of your sentence. Too many "me's" make the sentence feel clunky.
2) We say, "They are the kind of people who..." not "There are a kind of people who..." (I suspect you might have gotten mixed up, though, because "they are" can be contracted to "they're", so we could say, "They're the kind of people who inspire me," and the words there and they're are homophones.)
3) Yes, it's possbible to say "There are a kind of people who...", but, when we say this, we are simply saying that some kind of people exist. For example, "There are a kind of people who like to be mean on the internet. We call them cyberbullies." But you have already identified the people in your first sentence, so this is not the construct you want to use here.
Why do we use the definite article? That one's tricky. We could say:
There are a kind of people who inspire me. They are the ones who spread their enthusiasm.
This is proper grammar. In this case, we identify the kind of people we are talking about only after we mention that such people exist, so, in the introductory remark, we use an indefinite article.
Some people like to spread their enthusiasm. They are the kind of people who inspire me.
In this case, we have already identified the people we are talking about, so we use the definite article.
Also note, the "kind of" phrases can be removed, and the sentences retain its original meaning, because we can refer to "a kind of people" as "people":
Some people like to spread their enthusiasm. They are the people who inspire me.
However, when we try this with the first example, we need to remove the indefinite article in order for it to sound right:
There are people who inspire me. They are the ones who spread their enthusiasm.
Oddly enough, we can remove the article from the first one, too. The first one works either way:
Some people like to spread their enthusiasm. They are people who inspire me.
Incidentally, this is exactly the kind of question people were thinking about when they said didn't like using the word "basic" to describe ELL questions. Martha once said it in meta like this (emphasis in original):
Incidentally, the underlying assumption .. appears to be that ELL is for the easy questions and ELU is for the hard questions. THIS IS NOT TRUE. Both sites frown on very easy questions, especially ones that would be easily answered by a dictionary or thesaurus. The difference is that ELL is for questions that wouldn't occur to a native speaker, not because they're easy, but because it's something that a native speaker Just KnowsTM.
This was a hard question to explain! (especially the part about the articles)