Android Studio is the newer offering from Google, Eclipse is a general purpose IDE, initially developed for Java and which has an Android plugin. Which is better depends on a lot of factors, I have been using Eclipse for longer than I can remember so it feels like a natural choice. You may prefer Studio, why not try both and see, they are free.
Android Apps are developed in Java, although due to copyright issues Google don't actually call it Java.
I just got an Android tablet and looked around at all the apps that I could get; it must be in the millions! Then I wondered how the programming is done, and as I was making a trip to my local library, I took a look at what they had. There were several books on Android programming, even "Android for Dummies". They talked about the Eclipse system, and the language is Java, though I've also heard you can use C. Learning to do it might be fun, but I bet there would be frustration along the way. I think I'll let other people do it for me.
If you just want to try something relatively simple you could try App Inventor, it's free and very simple to program as it's all GUI (like Lego Mindstorms).