A client has contacted me out of the blue and he wants me to start shooting some footage of product demonstrations that will then be uploaded to youtube and their website.
Use a DSLR like the Canon 600D and choose your lens of choice based on the kind of product you are shooting. This is the cheapest and safest option. As for a solid editing system that is also cheap, I highly recommend Sony Vegas Pro (I use Adobe CS exclusively, but I have had experience with Vegas and I love its speed and feel). If Pro editing is not your thing, and you don't need fancy effects, the free Windows Movie Maker will also work!
The combination I've mentioned is good enough for youtube and the internet, and I also suggest you shoot in 720p, and not 1080p. The differences between the two on the internet are almost impossible to notice, and most people don't use full HD monitors anyway.
If you're based in the US, then a typical workflow would be: 720 at 24fps and 60fps (the latter for slow motion effects), edited natively on a medium performance PC (a core 2 duo is good enough). You can render your final output to the resolution and bit rate your client specifies. I suggest 24p since it will be played on the internet, and will allow you to maximize bit rate for the highest quality, when streaming or downloading.
Hope this helps.