Remapping function keys on MacBook (Air)

I'd love to be able to do something more useful with some of my function keys than the default set-ups of brightening the screen, the keyboard backlight etc.

For instance what I'd like would be for F5 and F6 (the keyboard backlight keys) to change the lighting only if combined with shift or the cmd key.
And then remap the keys so that, for instance, by pressing F5 I could switch to/open my Mail app [rather than clicking on it in the dock]. Or that simply pressing F6 might open a new compose message window in Mail.

I'd happily pay for software that lets me do this kind of thing, if necessary.
Thanks for any help.