As far as a dictionary is concerned, which may also be related to 'what to learn'), parts of speech fall roughly into two kinds, open and closed.
A closed set
is one that is pretty much unchanging. For example, the set of pronouns in English has I, you, we and only a few more, and a new one is rare ("y'all" is one of those rare exceptions. Pronouns, prepositions, conjunctions are closed sets; these all have small numbers in the dictionary (under 20 each).
An open set,
however, tends to allow growing in many ways. New nouns and verbs are created all the time, either in technical vocabularies or everyday slang. Nouns, verbs, adjectives and adverbs are open sets in English.
There tends to be a lot of growth of nouns. Combining words in a phrase into a single word is more accepted than for verbs (at least in English). For example "hand warmer" has moved on to "handwarmer" but if you want an action, you still just warm your hands instead of "handwarming". Informally, I think the reason for this is that there are more ways of describing objects than there are of actions.
I would rank the order in percentage as nouns, verbs, adjectives, adverbs, pronouns, prepositions, determiners. With nouns winning by far, but the last three disputed.
But the percentage of occurrences in speech is a different matter. 'the' is the most frequently occurring word in speech and writing. The frequency of appearance and the count in dictionaries is inversely proportional. There are more closed set terms in a text than open set terms. Also, the closed set is the glue that holds sentences together; without them, you just have a bag of words, you know that something did something to something else but not exactly which direction.
So if you're learning a English (and most languages), the vocabulary component is the hardest part, memorizing an unending list of new nouns and verbs for things like "windshield wiper" or "mitigate". You really must learn the closed sets first just to get the basics of communication, but the long road to (educated) proficiency is in the open sets, the nouns and verbs.
As to your exact question, what are the percentages, I'm basically saying that, for a growing language like English, the percentages are changing, the nouns and verbs always growing, which means they will take up a larger and larger percentage of the dictionary.