Handheld Audio Spectrum Analyzer

I'd like to build a small, back-lit, audio spectrum analyzer. Things I might need:

1) Micro-controller that does signal processing stuff along with associated software and development kit. Could be expensive. Nobody should have to code the FFT in this day and age. TI?
2) LCD (black and white is probably fine) that has a very simple input/output. All it needs to do is show the frequency axis and very thing Winamp-like bars for the magnitude. I guess we can skip the phase entirely and just have two buttons: On/Off and a button to freeze what's currently on the screen so you can examine the current spectrum at your leisure. Is touchscreen expensive?
3) Tiny microphone. Directional seems most reasonable, but it would have to work at large ranges, so maybe the tiny mics ones I used for my mini-disc secret headphone recorder would be better.
4) Casing, power supply. I can probably steal a bunch of stuff from work and might just be able to actually develop this during work. Hmm.

Thoughts from the ghosts that read this blog?