I think photo addicts could argue long and hard about what is the "most" important feature of a digi cam. Even though I started photography professionally in 1953 I'm still pretty much a newbie with this digital stuff.
I made a big misteak with my last purchase. I was so enamoured with all the features of the Olympus SP800UZ I just had to have it. Big disappointment. With this experience, I would say the most important feature would be simply being able to hold the camera. My Oly is simply not hand or finger friendly. Second, I (that's me) want an eye level view finder. This doesn't have one.
Lesson learned: never buy a camera without holding it and doing, at least, dry shots. I ordered online and denied myself that opportunity.
At the other end, my son has a Nikon that is only slightly smaller than my pick up truck but weighs about the same. When he goes interesting places with the family, it stays home and he shoots his wife's P&S.
Hold it, try it. If it doesn't shout that it is for you, it isn't.
"Folks is funny critters."
Think for yourselves and let others enjoy the privilege to do so, too. ~Voltaire