More or less any new computer in that price range will handle the things you've mentioned, but as you are obviously aware, the games performance isn't going to be up to the standard you would expect from more expensive machines.
Any new machine will easily handle Office applications.
The two things that will have the biggest impact on your other computing needs are the processor and the amount if RAM. Put your money into the fastest processor you can afford, and the maximum amount of RAM that your motherboard and operating system can use. The RAM is going to be important for your photo/video work.