+1 for Camtasia - I tired what feels like a zillion of these things a while back and while none was completely perfect, this was the best one for the price and got the job done.
One caveat -- on the mac at least, the audio recording / playback is not great, so you may want to download the free program Audacity for audio recording....then import that
audio into Camtasia and use Camtasia for the screen capture (it's almost impossible to perfectly sync voice + "doing stuff" on a screencast at the same time, and besides, if you try to click & talk at the same time, you'll end up with a bunch of "click" / keystroke sounds in your final recording that you may take quite a bit of time to edit out); it's sometimes just easiest to record the audio and video in separate
steps and then combine them, which Camtasia lets you do easily).
Finally, if you plan to do a lot of these, it might be worth investing in a stand-alone microphone (I have one from Audio-Technica), but if it's just a quick-n-dirty demo (vs. the core of your product) this might not be needed. Try Audacity or the native audio recording included in Camtasia and see if you think they are of sufficient quality.
One final note -- if you're going to record "Full Screen" on Camtasia, they do (again, this is on the mac version - not sure if it's the same on the Windows version) this infuriating thing where they, as a default, only record at 50% resolution (to keep file sizes small). Which hey, is great for file size, but frustrating if you want Very Crisp visuals. (to fix this -- something I only discovered on a techsupport thread months into using it!) Go to Preferences->Canvas-> and change the "Scale By Percentage" setting to "100%" from its default of "50%"
Side note: Re: Adobe Creative Suite, double-check the pricing ....(or, Christian, tell me how you got such a good deal, ha ha) -- I believe that Adobe Creative Suite is $50/month if you sign up for a full year, or something like $75/month if you just want to use it here and there. Might end up being cheaper than Camtasia if you only use it from time to time, and it does come with the added benefit of giving you access to Photoshop & other cool Adobe tools, which might come in handy for creating crisp graphics, etc.