THIS ALL DEPENDS ON WHEN AND WHERE YOU START, but for the summer this is what i would say.
With the ULA pack you will find that Nalgenes aren't the easiest to get in and out of the pockets. Plus they are heavy.
I suggest 2 SmartWater bottles. The shape works awesome.
I'm not sure what all is in your cooking set. But you might see if there is a way to not bring everything.
Also, do you have a spoon/spork
You may look at an alcohol stove
Ditch the Water filter, use bleach or aqua mira. That way you can fill up on the go, because the drops will fit in your hip belt pockets.
It would be nice to know what you have already bought, or are planning on getting.
Your pack seems to big. I suggest the ULA Circuit (its what i used)
I wouldn't use a pillow, i just stuff my fleece into its sleeve, and use that. works great
You still need: (with my suggestions in parenthicies)
Pack Liner=I suggest a trash compacter bag, and don't bring a pack cover
shoes: go with trail runners and don't bring camp shoes
Socks: Two pairs, I like wrightsock, built in liners. you need 2 pairs, second doubles as gloves.
Bear Bag System (Z packs Cuben food bag, small Rock bag, 50 ft. of ironware from lawson)
Fire Starter (big mini, only 1 no need to be redundant on the AT, you will meet tons of people to help out)
Hiking shirt (smartwool/icebreaker t shirt)
Hiking shorts/pants (patagonia ultra shorts)
long underwear pants (smartwool long underwear)
long underwear top (smart wool long underwear)
Fleece Jacket or Down Jacket (to many options. Go with Down or nano puff)
Rain Gear. (Rain pants double as wind/cold weather gear, if you only have shorts...I suggest marmot marmot precip (cheap, and you likely won't hike in them anyways. Rain Jacket--Keep it light, and breathable)
Guide Book (get the one with elevation profiles, its my favorite)
First aid kit: basically full of vitamin I and foot care stuff. keep it under 3 to 4 ounces if you can. Don't forget you can resupply on the AT every week if you need to.
stuff sacks: I like 1 small cuban/sil-nylon dry bag to keep my phone/Rx meds/notebook in, otherwise freely stuff everything into the pack.
smartphone. helps find food in towns or order emergency supplies to the next town with the internet.
Where to buy stuff:
Sierratradingpost.com subscribe to their emails. If you watch them smart wool can get quite cheap. Cheap rain gear options too.
hope this helped a bit