That is a though question, partly because you ask one question in the title and another in the post, but mostly because it depends on your definition of "importance".

Anyway, here's some interesting information on word-classes and relative importance of those in different languages:

• There are languages where adjectives could be considered "less important" because those languages don't have adjectives! (or at least very few). Instead of saying "the red car" or "the car is red" those languages could for example use a verb: "the 'red-ing' car" or "the car is red-ing". EDIT: Although I should add, since you used those as specific examples, that nouns and verbs tend to be pretty much universal across languages.

• I don't know what your main language is or how many languages you speak, but a great amount of languages lack an equivalent of the word 'is', for example in the clause: "the car is red". This is called a copula verb or simply copula. I guess you could say that copula verbs are "less important" in some languages, but I quite sure a lot of people on this subreddit would disagree. After all, what's really important here is not the word itself, but the relation between subject (car) and the predicate (red).

• An important thing to know about languages is that they mark words differently - they have different morphology. Chinese for example, doesn't mark their words at all (it's an isolating language), but Russian has several forms for the same word depending on its syntactic or semantic role in the context. For example: book is always "shu" in Chinese, but depending on if the book was the subject of the clause, the object or the direct object it would have different cases in Russian, eg. knig-a (subject or nominative), knig-u (direct object or accusative), or knig-e (indirect object). I don't speak Russian though so there may be more and they may look slightly different. Either way, my point is that in some languages this kind of marking (case-marking) can represent what are complete words or phrases in other languages, prepositional phrases in English sometimes become simply one word when translated to for example Finnish.

Wow, that's a lot of words o.O

I have absolutely no idea if that answered your question or not, my terminology is probably not spot on either, but any rlinguist is welcome to correct it.

TL;DR: What words are important in some languages may be less important, or even redundant, in other languages.