There is an abundance of water along the Applachian Trail. Whether it be from natural creeks running through the mountains or from a pump at a shelter, you should still treat it before you drink it. Cryptosporidium and giardia are bacteria common in water up and down the east coast of the United States and both have the power to end your long hike early. Its very rare for either to cause death but they are very nasty to deal once they are in your system. The good news is both are easily prevented.
Old methods of treating water consisted of using bleach, iodine tablets, or chlorine tablets. All of these are effective but over an extended period of time can be harmful to you. The most effective way to treat your water is to use a pump water filter or a UV light purification system.
A water pump is easy to use and will take most everything out of the water. The down side to a pump is the amount of time it takes to put the pump together and take apart each time you use it.
The newest trend in the market is a UV light purification system. It is as simple as stiring the UV light source through your water bottle for the prescribed time. The only downside is it is a battery powered product and if you are pulling water from a stream you need to prescreen the debris out.
How you store your water is up to you. Most hikers will have a water blatter in their pack and a few water bottles.