Launching Fallout 3 from Galaxy, Fallout 3 launcher appears, "Fallout 3 will now detect your video hardware and set video options accordingly." When I click 'OK', "Video settings have been set for High Quality.". After I click 'PLAY' after dismissing the dialog box, however, after a few seconds, the launcher reappears, detecting video hardware configuration again. The game itself won't launch. Even launching the game from fallout3.exe yields the same loop. Attempting to play on a Lenovo IdeaPad 110-15IBR

intel Celeron N3060, 4GB RAM (no clue about the specs), intel HD Graphics (no model info given by CPU-Z)

The problem is your Intel integrated graphics. See:
https://www.gog.com/forum/fallout_series/gog_version_of_fallout_3_really_works_on_win10

Ahhhhhhhhhhh, okay. Sucks, but yeah, I know FO3 works on Win10; I had it installed on my AMD rig at home. I just wasn't sure if a recent update, or indeed, the fact that I had just updated my laptop to 1903. I'll still give the link a looksee, though. Thanks.

Hopefullly you have learned a lesson from this;always read the requirements before you buy a game.
The GOG page for Fallout 3 plainly states it does not support INtel HD processors.

So I tried all of the standard fixes for this issue. Compatability adjustment, GfWL, resolution adjustment and switching between my Intel and Nvidia processors, no matter what I was stuck in the 'video settings.......quality loop'. This is how I fixed it,
-Went into the Fallout 3 settings on Steam and disabled allow Steam overlay.
-Went into my files and made a new folder under This PC> OS(C:)> Program Files (x86) and titled it GotY.
-Went to the default Fallout 3 location under ... Program files (x86)>Steam>steamapps>common and opened it 'select all', 'copy to' the new GotY location.
-I had to give it permission to allow it through my Bitdefender and then it worked.

My resolution was on default and my compatability was windows xp

I am running it on Nvidia GeForce GTX 1050
My computer also has and Intel core i7