Where are you going? Super hard to comment without knowing what environments you will be in. I would say no to shorts, they don't really wear them in Japan so you'll stick out like a sore thumb in most places. Get really comfortable shoes, you'll walk a lot even if you are just staying in Tokyo. In terms of socks, how often do you aim to do laundry? For shirts, I would consider bringing at least one button down but again it really depends on where you plan on going. You don't have to dress up unless you are going to a fancy restaurants, but maybe for a club the button down would be useful.

I've been backpacking before and I suggest bringing as many lightweight, breathable items that dry as fast as possible. If you carry around all your junk in a backpack for 35 days its gonna start smelling... not right. Especially if you are moving around a lot. I actually didn't bring a lot of jeans with me, just a lot skirts and lightweight pants - although this doesn't apply to you, lightweight cargo pants with pockets are actually a good idea. Have a look around at the mall and see if you can find any pants that are breathable and oh yeah WRINKLE RESISTANT! is important too.

For 30 days, I took something more like this, but then again I'm a chick :) http://www.amazon.com/TETON-Sports-Internal-Frame-Backpack/dp/B000F38YIM/ref=sr_1_10?s=outdoor-recreation&ie=UTF8&qid=1380230094&sr=1-10&keywords=large+backpack