@nvhstosu Since you stated you don't know much about computers, an important aspect to consider is the processor. Many people don't take a second look at it, but it's the brain of your computer and will determine how well your computer works down the road. If you have a strong processor your battery will last longer, as your computer will not have to work as hard fulfilling requests when you are doing things such as photo editing and listening to music at the same time. Intel's new core i3, i5, i7 family all have smart performance and adjust to your needs. The i5 and i7 come with Turbo boost, which speed up your computer when you need more performance/ power. This will save you from the typical freezing and drag on older computers. Buy investing in a stronger processor now you can insure that your computer will be ahead of the curve, able to handle new technology, and capable if you decide to get into more advanced usage such as video editing.
For what you are going to be using the computer for, I think any of these computers like the Gateway ID and NV series would work out fine with an i3 processor. The HP Pavilion dm4t series looks like your best bet. For $729 you get an Intel i3, 500 GB hard drive, 4GB ram, 600 cell battery (6.5 hours, web cam and even a cool little finger print reader. Similar to what R.Profitt was saying the rule of thumb is replace your computer every three years. I had a Dell Inspirion in college 2 years ago and around year two I had to have my computer plugged into the wall to even turn the computer on. So I would invest in a warranty for about two years, fix any problems you have with the warranty around year two and you should be good to go.
Hope this helps!