As I see it, best and most are both superlatives, and each can function as adjective or adverb. Adjectives and adverbs can be positive, comparative, or superlative. Adjectives are: good, better, best, and some, more, most. Adverbs are: well, better, best, and some(somewhat, sometimes),more, most. Here are some sample sentences:

Adjectives:
I wrote a GOOD essay; George wrote a BETTER essay. Who is your BEST friend?
May I have SOME juice? MORE juice, please. Which boy drank the MOST juice?

Adverbs:
Emily sings WELL; Marge sings BETTER; Joe sings(the)BEST.
Do you want to travel?(SOMEWHAT-this is usually understood, I think) I hope to travel MORE this year. Where do you want to travel MOST?