Choosing a video codec for screen recording

One important thing to consider when capturing a mostly static screen (desktop recording) is to use the VBR (Variable Bit Rate) option over CBR (Constant Bit Rate), in my case it reduced video size nearly 10 times without losing quality (the video stream average bitrate became comparable to the audio stream =-D).

H.264 has such option, but you have to set it manually, as usually default is CBR (at least in OBS Studio). If you use command line, ffmpeg has CRF (Constant Quality) by default, which also works pretty well for non-camera recorded videos.

Master copy
Lossless - HUFFYUV in AVI is a good option.
Lossy - MJPEG (series of JPEG) in AVI is a good option, where each frame will be independently encoded. The editing will be faster.

Distribution
Video codec - Use either H.264 video (not free) or VP8 (free video codec by Google). You should use codec with inter frame compression as screen recording tends to have a lot of similarity across frames, hence allowing for a better compression. Both VP8 and H.264 support inter compression where as MJPEG does not.

File format - Depending on video codec, you can use either MP4 or MKV file format. H.264 is more often encapsulated in MP4 container and VP8 in MKV. Google WebM format is subset of MKV format.

Subtitles - SRT is good choice for external subtitles. MKV supports internal subtitles if you want to embed subtitles inside MKV file as a separate stream.

Frame rate - 24 fps is good enough frame rate for your use case. You can actually use even lower frame rates if needed.

Bitrate/Compression level - Depends on resolution of the video. You should be able find good tutorials which provide which bitrate is best for given resolution.

Support - MKV with VP8 will play on Windows (Windows Media player) and Linux provided necessary software is installed. VLC Player is available on both Windows and Linux and plays MKV with VP8 without any issues.