The bracket most likely to win is the one where higher seeds always beat lower seeds: That is, after all, what the seeds mean. So you would fill out such a bracket, then ask yourself “What is the probability of a 1 seed beating a 16 seed”, and take that to the 4th power, and then “What is the probability of a 2 seed beating a 15 seed”, and take that to the 4th power and multiplying it by your previous number, and so on. Then continue into the next round, with a 1 seed beating an 8 seed and so on. Once you get to the Final 4, you’d need to use something other than seeds, but there are still rankings available on which team is more likely to win.
Of course, there’s a complication in this. This is so obviously true, that there are going to be a very great many people betting on the no-upsets bracket. And presumably, the challenge specifies that if more than one person gets a perfect bracket, they split the prize. So your expected winnings are much higher if you instead mix in a handful of upsets, in places where nobody else has them (at least, not that exact same set). How do you pick those? There can be no single clear answer, since if there were, everyone would do that one, and it would become a bad choice again due to prize-splitting.