I would recommend Open Broadcaster Software (called OBS for short) https://obsproject.com/ I would guess that 90% of streamers use this. It's easy to use and can capture literally anything from your computer into a nice little video file.
Best quality: Take the window that you are recording and crop it before you start the video and record. If you hit 'edit scene' you can drag the window capture around and even crop it by holding ALT when you click+drag a corner. Here's what my obs looks like http://puu.sh/qez6H/cb00e905f7.jpg
(dont forget to mute the microphone imput also whenever you are recording audio unless you want us to hear your heavy breathing)
Hope this all helped
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