I sometimes use Microsoft Screen Recorder for full screen captures. It produces very small files, but in WMV of course. Some people can't play WMV when you email the files (yes they are that small), but YouTube can import them.
For recording a browser tab (or fullscreen), I sometimes use Screncastify. It records in standard WEBM which is HTML5 compliant and it can automatically save to your Google Drive for sharing. It's a bit cumbersome to figure out the options and how to set it up as most Google software is, but it seems to work. The free version is only limited to 10m however.
There is also Wink but that generates FLV files. They are very small and you can edit them and add annotations, but I favor the more common regular file formats for sharing. YouTube can't import FLV files (if I remember). You could probably transcode the file with VLC or FFMPEG, but I haven't tried.