Windows Software to record from Webcam & Screen
Personally I use Camtasia Studio and SnagIt. TechSmith, the vendor, has created their own codec for their software which IMO works excellent.

You will probably find Camtasia a bit stiff when it comes to the price compared to your budget, but I mentioned SnagIt for this reason although it's primarily to capture screenshots it do have built-in video recording as well using the same codec as its big brother.

It's simpler and you will probably want to convert the result and edit it in a third-party editor (Camtasia Studio comes with its own editor which is in part why the price is higher).

I never recorded 3 hours but I did more than an hour which was without problem. The key factor here is to have enough space on the disk you record to.

My 2 cents..