There is no such thing as "the best" IDE. It all depends on your personal needs and preferences which is why you are the only person that can tell which one is best for you.
IDEA, Flash Develop, Flash Builder; pick whatever suits you.
Luckily all of them do come in trial versions as well.
To get you started with the setup process, make sure to download the latest AIR SDK. The Flex SDK isn't required for the vast majority of use cases, though some packages like remoting might become handy later on, but for now, just stick with what AIR provides.
Just remembered, Josh made a setup guide for IDEA. Just adapt that for Starling and you should be good to go; http://wiki.starling-framework.org/feathers/intellij-idea