No need to step up from Audacity, unless you want to spend hundreds of dollars.
I have Sound Forge Audio Studio 10, and I prefer Audacity.

Plug and play special effects are a pipe dream.  You'd still have to get your hands dirty to create certain special effects.  The most intuitive software out there is the power of your imagination.  Outside of that, you have to make the effort.  With that in mind, you have pretty much what you need for free.  Beyond that, there'll be people suggesting "get After Effects, get Maya, blah blah oink oink".  If you're using Blender, then you can accomplish whatever effects you want for free.  You just have to put in the effort.

http://www.blenderguru.com/videos/how-t … -explosion
http://www.blenderguru.com/videos/how-t … amethrower
http://www.blenderguru.com/videos/how-t … zzle-flash

There is a list of free software in the forum.  If you've already checked on that, then I think there's not much else we can suggest for you.

I will echo on what the others have said; Audacity is a fine audio editor, and I really don't see the need of getting something grander (Unless you're a professional). I also agree with what Lechnology said; it's not about the software, but what you do with the software. Blender is perfect for most CG needs, and as long as you're dedicated to put the time and the effort into it, then you'll most likely get some good results.

Also, I think you should practice some more on CGI before you make the actual film.

I suggest Vurtual Dub or MPEG Stream clip for editing. Both are free and work surprisingly well.