If you're wondering what brand to get, Lenovo is generally considered to be 2nd (next to Apple, naturally), and they just so happen to have a decent sale on Thinkpads, Ideapads, and Essentials
for the next few days.
Nothing you stated demands a powerful system really. Uploading photos depends more on your internet connection than your computer, and if your primary purpose other than that is typing essays then you probably don't want to go too small. A few essays on a tiny laptop will start to get tedious real quick.
I would suggest checking out both the Thinkpads and the Ideapads. If you do opt to go for a smaller one, I might suggest also getting a separate USB keyboard for when you're not in transit to make all that essay writing a little less uncomfortable.
As for the hardware... Don't worry too much about processor speed, they're all going to fit your needs. If you end up with money to burn and want to beef it up a bit, I would suggest either more RAM, or if you don't think you'll need a huge amount of storage space, a solid state drive as opposed to a conventional hard drive is an upgrade available in the Thinkpads. A solid state drive would add about $250 to the base price, and can't hold nearly as much data, but is lighter and consumes considerably less battery.
You shouldn't have any problem getting something that fits your needs for under $1000.
My girlfriend has had an Ideapad for a few years and it has traveled to over 40 different countries with her and is still going strong. I'm personally a fan of Alienware, but they honestly aren't worth the price for most purposes, I just like to splurge.