I've seen some really nice stuff made with Gamemaker, but I'm sure you'd need to learn some of the scripting for that. If you're not wanting to mess with any type of coding you're going to be pretty limited, but Gamemaker seems to be a good choice for that (I haven't used it much myself, though).
Yup Stencyl is based off of Flixel, though that route would be more programming intensive. If you go into programming there are tons of other options as well. Flashpunk, another Actionscript 3 game library like Flixel. PyGame for Python. Python is very useful as a scripting language in many 3D apps. Love for Lua. Slick2D…
I've heard Gamemaker is good because you can start off without needing to code at all. Then as you get more comfortable with the concepts you can start to learn how to code through it's scripting language. There's Stencyl which I've heard is similar to Gamemaker but works with Actionscript 3 the language of Flash under the…