I'm not sure what your website is providing but I would imagine that a screen capture video demo works best most of the time as it allows you to showcase your products nicely. For this on the Mac you can use things like SnapzPro and MousePose (take a look at the Firebug screencast).
I'm not aware of any companies to use for a full production video. As far as tools go you can probably use any decent camcorder, a tripod (handheld video doesn't look very professional) and some video capture software. There are plenty of options depending on your platform. Once you shoot your video however it should be very easy to outsource the editing if you're not comfortable with it. You can usually find talented individuals in other countries willing to do this cheaply (ask for samples, etc).
I just did a screencast (ironically it's the item just above this one right now- http://news.ycombinator.com/item?id=54774). We pursued your "option 2" initially and ended up doing just the screencast for our homepage demo on jumpbox.com.
I work on a Mac and used iShowU for the capture and edited and produced it in iMovie. Our homepage video is just a quicktime file. For the screencast in the tutorial above I used the Adobe Flash FLV converter to turn it into an flv and wrote a small custom media playback swf to do what you see here-> http://video.jumpbox.com/?app=trac
Please, whatever you do, don't host the video on YouTube. (Ahem, Wesabe.) To me, nothing says "I love compression artifacts" and "I can't afford to host my own site" more than YouTube.
I liked the idea of Snapz Pro until I discovered how difficult it is to edit footage losslessly. For our last screencast at the office I think we used Camtasia.
I'm thinking about 2 video types: 1) purely screen capture video demo to showcase software OR 2) a full-featured video with people, dialogue, transitions, etc--basically a full production demo.
I'm leaning towards option 2. In that case, if I were to do it myself, what are some high-quality software programs that I could use? If I'm looking for professional help, what companies or services would you be able to recommend.
You can take a screencast with Camtasia(pretty popular with internet marketers, not that bad...).
Then edit with basically any program...I like ArcSoft - ShowBiz for starters, it's easy and has alot of features. Or if you have a bit more video editing experience Adobe Premier or After Effects should help alot! Or if you're on a Mac...FinalCutPro for professional editing.
I'm not aware of any companies to use for a full production video. As far as tools go you can probably use any decent camcorder, a tripod (handheld video doesn't look very professional) and some video capture software. There are plenty of options depending on your platform. Once you shoot your video however it should be very easy to outsource the editing if you're not comfortable with it. You can usually find talented individuals in other countries willing to do this cheaply (ask for samples, etc).