is most important to you ... this makes sense as in selecting something say a bag you want a red bag it's important the bag is red small in size that is important to as it's your preference in this case it's personality let's say you owned a dating website you now have men and women that have different personality and interests. it's important to match the interests and personality to be similar . so you would ask your customers what personality is important for your future partner to have ?

Well, "best" and "important" are both adjectives, and they are used to express characteristics of a noun. In your sentence, the noun is "personality", and you should choose only one adjective to refer to it. Using two adjectives with similar meanings in a row makes no sense. Also, you could use more adjectives to refer to various charateristics of the noun, but it doesn't seem to be the case. However, you could use an adverb to emphasize your idea, for example "most important" or "most beautiful", etc. Eventually, you could say "what kind of personality is the best to you" or "what kind of personality is important to you".

You could also say, "what kind of personality is the best to you" which would mean the personality you like the most and think is the best. And saying " what kind of personality is important to you" basically means the personality you'd like the most, the same thing, it's just the word "best" and "important" you'd choose but writing both would be confusing