VIDEO RECORDING & EDITING
As a math teacher, one of the most helpful video tools I have found is not to video myself, but instead to video - or capture - the screen as I am writing on my laptop tablet or on a whiteboard. Especially in introductory lessons, students in math class need to see step by step how a problem is solved and video capture is my prefered method for this.
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If you have OneNote, there are embedded options to record audio and video. If you have OneNote, or something similar, but do not like the built-in feature, a free trial is available for Snagit, and with a one time fee of $50, even this public teacher was able to afford it. (I quite like it!) Another option for whiteboard tablet simulation with a free option is Educreations.
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Don't discount built-in Windows applications either. For instance, one of the easiest and free! video-editing applications I have found is the built-in Windows Video Project editor. When I take videos with my phone and need to stitch and edit them togther, or edit OneNote video captures, it is quite good! I have even used it to edit a video and then over-dub a running audio commentary on top for a seemless video!
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Also, don't forget about all the free resources already available for your use on the web (Khan Academy). They may not have your own personal spin, but in a pinch, why recreate the wheel?
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Finally, should you have more funds you should definitely explore Articulate's Rise 360 or Adobe's Captivate and Camtasia! But note, in addition to their hefty price-tags, these programs are super-powerful and thus have a bit of a steep learning curve before you will be able to take full advantage of their capabilities.