I didn't remember the exact numbers so I recorded my desktop three times, once in 80, once in 90, and once at 100 quality for Motion JPEG, here are the results.
This shows you that you can get slightly better quality for very little file size, so why not? Obviously the jump to 100 quality is a huge hit to file sizes which is why I don't use it.
Note that I'm doing this in 29.97 FPS which shouldn't make a huge difference, but seems to be the better option from what I've read. I responded to you about my headset on YouTube but I'll mention it here as well. My headset gave some nasty hissing over 3.5mm and I was not interested in editing the audio to remove hissing every time I made a video. So I played around and found that over USB there was zero hissing, so if you don't have a USB headset I recommend getting one. I did zero audio editing in the YouTube video that you watched.
If your file size doubled after rendering it in Premiere Pro then you're using the wrong codec/settings. For my tutorial video that you watched, the footage before editing was 2.7 GB and five minutes long. After editing it was 3 1/2 minutes long and came out to 313 MB when rendered as an .mp4 in 1080p using Sony Movie Studio (it's a budget version of their Vegas movie editor). That is what I uploaded to YouTube.
MPEG-1 in 720p at 40 quality seems like it would be very low quality, but maybe I'm off base here. Note that my video of similar length came out to a similar file size using higher quality settings and a higher resolution. I think it's not what you're recording in Bandicam that's the problem, I think you're using incorrect rendering settings in Premiere Pro which are causing the exported videos to be unnecessarily bloated in size.
I think my 3 1/2 minute video in 1080p took roughly 10-15 minutes to render. I have a pretty good machine though (freshly built) but I still think your settings are off in Premiere and fixing those would likely do wonders. What file format are you exporting them as? And note that sometimes there are multiple ways to export a file even if they use the same extension so that doesn't always tell the whole story. Maybe you can find comparable settings in Premiere, here are the options that I use in Sony Movie Studio when rendering for YouTube (note that these are all default settings for their "Internet HD 1080p" rendering option, so I didn't change anything).
Description: Use this setting to create an MP4 (AVC/AAC) file for progressive internet downloads.
Audio: 192 Kbps, 48,000 Hz, 16 Bit, Stereo, AAC
Video: 29.970 fps, 1920x1080 Progressive, YUV, 12 Mbps
Pixel Aspect Ratio: 1.000
The file exports as an .mp4. Unless you're attached to Adobe Premiere I'd recommend trying out Sony Movie Studio. I'm assuming you either have a student discount or torrented it since Premiere Pro is insanely priced, and Premiere Elements isn't very good from what I hear. Sony Movie Studio is a budget version of Sony Vegas and you can get it legally for around $75 which is why I went with it (it's also highly reviewed). I'm actually still on the free trial but I'm definitely getting it. Glad someone found my video useful, and I'm sure you'll have plenty of new information to digest in this huge post.