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Adaptive High Bitrate will give you a lower file size by increasing the compression (= lowering the quality) in parts of the video that don't need it, but for local playback this is not really an advantage. Depending on the playback machine you should try the High bitrate first. The ones you should be looking at are the ones called Match Source- bitrate. There are numerous presets available, but most won't be relevant because of the unusual dimensions of your video. In the Premiere export window choose H.264 as the format.
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H.264 in an mp4 container allows for small files with good visual quality, the ability to tune the settings to achieve tradeoffs between size, compatibilty and quality, and almost universal playability with modern devices. For playback the best codec is unarguably h.264 (AKA MPEG-4 Part 10, or MPEG-4 AVC, or just plain 'mp4').
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