Just make sure to a hair straightener with ceramic plates. Ceramic plates have a more even heat distribution across the plates surface which means that the whole plate is an even temperature. The temperature can be controlled better, because ceramic plates heat up and cool down quickly. As temperature is crucial, it will be important to your fine hair.
Also you should be putting some type of thermal protectant on the hair before you dry your hair.
When it comes to hair straighteners, it's better to get a best one for your hair at the beginning terms, or you'll pay for it later. Please go to hair straightener category, we have reviews on almost all the popular straighteners. And see a before and after picture and then judge for yourself.