AVI but it is pretty much obsolete.

Quote AVI but it is pretty much obsolete.

Yeah, especially for a finished product. If you have HD or 4K clips, you'd really want to use those resolutions for making H.264 or H.265 clips in MP4, M2TS or MKV containers.

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AVI can be best used as a restoration vehicle, it can carry a ton of color information.
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Ok, I kind of see. But let me say this:

1) most of the videos I will be doing will be shot from a Samsun Galaxy Note 8

2) The purpose for most of the videos I will be doing will be to be placed on YouTube

3) I noticed that with this first video I produced, I did it in .AVI format, and I am noticing that the "Screen Record" portion of my video does not really show the letters and stuff onscreen (the content of that portion of the video is such that I am surfing onlin and clicking some links, and there is various pieces of text sown there, and whatnot) . Would another file-format, besides .AVI, be better for clearly showing the text on the browser parts of my videos, such that the text on-screen at that time is more legible?

4) If MPEG-4 is better, maybe I am missing something, but my chooser when I am the "Produce" portion of my Power Director 17 is just showing "MPEG-2"..? Where's MPEG-4? If I don't care about file-size, should I always go with the larger width-setting, when there are multiple different sizes for the same resolution?

You're literally in the wrong technology decade by looking at the legacy MPEG2 and AVI choices. Those are from the 90s when DVDs were considered "high quality." Also, it's the resolution of the produced video that matter, and those two choices are really only suitable for content on old-style analog TVs.

These days, you want H.264 or H.265 to handle the video from any modern device. You'll want at least 1920x1080 pixels or higher to get decent quality produced clips. It doesn't matter which container (file extension) you use, MKV, M2TS and MP4 all support the high resolutions you need.

YouTube/optodata

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Quote Which is higher quality, AVI or MPEG2?

AVI and MPEG-2 are both container formats and do not necessarily specify which codec is within it. They will vary in limitations as to how many streams and of what kind can be contained within it, but they do not directly affect the quality itself.

For instance, you can store a h.264 stream in MPEG-2, MPEG-4, MTS, and TS.

https://en.wikipedia.org/wiki/Audio_Video_Interleave