The reason why Hermione chose the cloak is pure logic and logic alone, and the story of the three brothers only reinforces that which can be figured out purely by logic.
What's the stone good for? Nothing really. It can't really bring back the dead only their spirits who apparently grow tired of being summoned back to witness the living, and there is some real consideration about whether the ring truly summons the spirits of the dead to you, or whether they are an extension of your memory and desire to see them. (Similar to the mirror of Erised).
The wand, although an extraordinary tool to increase the power of your magic, has the unfortunate side affect of pitting you against any and all wizards that crave for more power. You will be forced to live the life of involuntary duels.
The cloak on the other hand is not coveted, its use is defensive in nature used for concealment, and to avoid or flee a fight. Chances are it's the one instrument of the three that will do the owner the most amount of good with the least amount of consequence or regret over that decision.
It makes the most sense logically that the cloak would be the most desirable hallow of the three, and Hermione being driven by logic rather than emotion or whim would not only chose the cloak but assume anyone else with one bit of logic or intelligence would also chose the cloak.