There is no such word as
bestest in formal English. Bestest is erroneously formed by applying the suffix for the superlative, -est, to best -- but best is already the superlative, so bestest is essentially making a double superlative, where logic only allows one. The phrase most best is also incorrect, for the same reason.
Best may also be a (transitive) verb: 'to best' means 'to gain an advantage over, to get the better of, to defeat'. (Curiously, the verb 'to worst' (formed from the adjective 'worst', i.e., the superlative of 'bad') has the same meaning as 'to best'. See further worsted.)