Why was a simple magical object like an Invisibility Cloak put with two other great magical objects like the Elder Wand, and the Resurrection Stone?
There's a reason why these legendary items were called Deathly Hallows. They let their wielders gain "triumph" over death. The cloak was technically the most powerful among the 3 because it hides the wearer from anything, even Death himself. According to the legend, its original wielder was able to dodge Death his entire life. After living a long, wonderful life, he decided to pass on the cloak.
The elder wand, though powerful in itself, turns its wielder into a likely target for challengers, and wizards have been murdered in their sleep for it. The stone, well, brings the dead back to life but they come back as "zombies." Dumbledore found that out the hard way.
In the book Harry Potter and the Deathly Hallows, Harry and Hermione learn from Ron and Xenophilius Lovegood about the nature of invisibility cloaks.
An average invisibility cloak is usually a travelling cloak imbued with a Disillusionment Charm, or carrying a Bedazzlment Hex, or else woven from Demiguise hair, which will hide a person initially but fade with the years until it turns opaque. Charms wear off cloaks or they get ripped apart by spells so that they have holes in them.
Harry's cloak, on the other hand is a true invisibility cloak, in the sense of being able to completely shield the wearer from sight, and cannot be worn out by time or spells. That's why when the Death Eaters try to Summon it in Hogsmeade, the cloak does not react.
Harry's cloak is immensely old, but is still perfect in every respect. It renders him (and anyone else) completely invisible so much so that they were never caught under it.
It depends on your own mentality. I think JKR herself hashed out the argument, when Harry, Ron and Hermione chose which hallow they would like to possess. As Far As I Remember, the arguments went like this:
Ron: The wand. It would make me immensely powerful.
Harry: The stone. I could call on Dumbledore for advice.
Hermione: The cloak. We would be safe from Voldemort.
Ron, the most aggressive, chose the wand. Hermione, the most cautious, chose the cloak. Harry, the most confused, chose the stone. So, depending on your mentality, you would each prefer a different hallow. (Sort of like how those RPG games let you customise what things your character specialises in.)
Personally, I don't see the point of the stone. You can always use a shield or a weapon, but you don't always have dead people you want advice from.
As the story of the Deathly Hallows states, it allowed the user to hide from death. The other two objects lead one to take chances, but you can only use their power so much. The cloak can hide you, so long as you are careful. And as was said, it's the only perfect invisibility cloak around, thus making it more valuable.
I don't have the quote handy, but one special thing about the Hallow Invisibilty Cloak that made it special was that it shielded other people together with the owner.
A second unique property was the fact that it was resistant to charms/jinxes/hexes aimed at negating invisibility.