The teacher should be the Buddha at the least.
As to the teachings, it is difficult to say. Each school believes theirs is the correct view, but also each school has created a "self" of history, ritual, traditional and cultural connotations, the texts they choose to accept or ignore if any, etc.; it is rare that we recognize this "self", which like our own mental construct of a self is merely an illusion supported by attachments.
All schools of Buddhist thought teach of suffering and its cessation, and this is that teaching which is irrefutable; seeking liberation is Buddhism. Whether for only yourself or for others, we must at least find our own peace that we may know the way and be proper guides.
The intent of the individual is of utmost importance. Let one who chooses this school or that school do so because its way of teaching the Dharma is in accord with his or her personality and temperament, and so also their ability to understand on a personal level.
I have come to know more and more individuals who profess they are followers of the "Buddha-Dharma/Dhamma" as opposed to of a particular school, meaning that they at the least understand/practice the core concepts of Buddhism: The Four Noble Truths, The Noble Eightfold Path, Impermanence, Non-Self or Selflessness, Depending Origination (or Arising, Co-Arising, etc.), Dukkha, Karma/Kamma, Nirvana/Nibbana, Rebirth, Samsara.
I'm partly of this myself, but I also accept that the different aspects taught by each school have their own merit, and in regard to "supernatural" aspects that can be neither proven nor disproven, I've found that not having a belief does not make requisite disbelief. Instead, one can understand on the conceptual level, literal and metaphorical, and exist in the peace of neither belief nor disbelief.
Strange world we live in, eh?