Well, like mrcharly said, you can climb in just about anything, and people have. That being said, the right gear will make things much easier. To chose the right gear, you first have to know how you plan on using it. The more you push yourself, the more the gear starts to make a difference. If just walking about on a weekend trip, just about anything will do. If you want to do some serious climbing up those mountains, then you need to chose more carefully in terms of weight, compactability, durability, and fit.
I use an Arcteryx Beta SL jacket. It is light at about 11oz, it is very tough, which I need for when I am scraping against rock or glacading down, the hood is helmet compatible, the pockets are harness compatible, and it has good closures. It is a GoreTex jacket. There is no magic there. It's just a lightweight, strong, and well made jacket.
There is no overall perfect jacket or perfect material. Figure out what you want to do, then then get the shell that best fits that function. The easiest way to do that is to look at what people who do similar types of trips are wearing.