If possible, I recommend you go with the Lenovo G50 laptop with the A8-6410 APU as suggested by joshyboy82 for $280. The APU is pretty close to the performance of an Intel Core i3 CPU and the integrated graphics core is about as powerful as an Intel HD 4000 which is pretty decent given the price of the laptop.
For something closer to your $200 you will be getting a pretty low performance laptop running Windows. An example would be the 11" HP Stream 11 and 13" HP Stream 13. They have the same specs with the exception of the size. You basically get 2GB of RAM that cannot be upgraded, 32GB of solid state storage known as eMMC which is about equal to the speed of a standard 5400rpm hard drive. With such limited storage you will need...