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.
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.
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!
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?
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.