A culmination of suggestions found on various forums and months of my own tweaking, these .ini settings for Fallout 4 should get the game running well on even an older gaming rig. Includes 4 fully hand-tailored presets to suit different target systems. Anyone who tries these settings should experience the following:

• Significantly higher average framerate and feeling of "smoothness"
• Less significant frame drops in complicated areas (downtown, Corvega, etc)
• Visibly shorter loading times
• Increased game engine stability (based on personal experience - your mileage may vary)
  

Remember to bypass the launcher and start the Fallout4.exe program directly, or the launcher may overwrite the settings!
You will need to customize your mouse sensitivity, do not make the files read-only until you have done this!
Additionally you will need to use NMM to reset your load order after installing this - it is stored in these files!

Overview of the Presets

• Low Preset: This is aimed at getting the game to run on a toaster. This means REALLY old systems, and more modern systems with integrated graphics (such as Intel chips, AMD A-series systems, etc). View distance is VERY low, and only minimal mip-mapping is done on the textures (meaning they will be rendered at a very low resolution - 16 passes are skipped). This preset also uses FXAA instead of the standard TAA setting in all others.
• Medium Preset: Aimed at old gaming rigs, this preset is built for systems with 4-8GB of RAM and 3GB or less of GPU VRAM. You can see a comfortable ways off into the distance, and more texture mip-mapping is done (12 passes are skipped). This preset is aimed at delivering good performance without actually sacrificing too much visual quality. I RECOMMEND MOST PEOPLE TRY THIS PRESET FIRST.
• High Preset: This preset is for systems which have room to improve over the medium preset, but still struggle with the game in its out-of-the-box form. View distance is somewhat higher than the medium preset, and shadows are rendered at a higher resolution (though still in single-split mode). Texture detail is the same as Medium (12 passes are skipped) since this really helps GPUs with a small amount of VRAM (3GB or less) run the game without crashing.
• Ultra Preset: For systems that still have room to push over the high preset, the Ultra preset is essentially the same as the High preset, but enables God Rays (volumetric lighting), Ambient Occlusion, and Bokeh Depth of Field. This preset is appropriate for systems that are "almost there", but are not quite meeting performance expectations with the default config. It should look visually nearly the same as it does out of the box, only giving the system the advantage of less mip-map passes (12 skipped) and single-split shadows to lighten the overall load. This preset should work well for systems with a modern "budget" GPU which has less VRAM than higher-end cards, yet more than most previous-generation GPUs (such as a Geforce GTX 1050 Ti or a Radeon RX 570, both of which typically have 4GB of VRAM).
  

A more exhaustive list of the settings that are customized:

Dynamic shadow map configured to run in single-split mode - shadows for fine objects tend to be somewhat blurry, but radically improves performance overall - also removes the annoying transition from low to high res as the player moves closer to distant shadows
Ambient Occlusion, Depth of Field, and "God Rays" (volumetric lighting) disabled
Engine configured to run in unbuffered vsync mode (vsync remains enabled but no frames are pre-rendered - this keeps the framerate unlocked and input lag low while still capping the framerate at 60)
Temporal AA enabled (how could you not? soooo pretty)
Actor, Item, and Object fade distances set to maximum default levels (15,15,15)
LOD boundaries hand-tooled to go with the block loading distances (view distance)
Disabled features that sap performance without visibly doing much (rain occlusion, lens flares, subsurface scattering, radial blur, etc)
Pushed the grass load distance out a lot
Disabled all NVFlex features (unsupported on ATI, may sap too much performance on lower-end nVidia)
Probably other minor stuff I'm forgetting.

Changelog

v1.1 now includes four presets available for download - Low, Medium, High, and Ultra shadows. For older systems I recommend the Medium preset - it should provide an optimum blend of visual quality and performance. Newer systems can probably use the High or Ultra preset (but be warned, Ultra is very likely to show some performance impact, particularly in large interior locations! If you want to test for this, visit the Boston Public Library - in my experience this is one of the worst-performing interior cells).

v1.2 makes a few changes to increase overall performance and visual quality - light and specularity LOD now applies at the edge of the level 0 block (the area loaded at full detail around the player), rather than the edge of the level 1 block (the first LOD ring). The level 2 and 3 LOD rings have been extended significantly, providing a much better view of distant stuff. Finally, the number of mip-maps to skip is now 12 rather than 16 - based on my observations, the game does roughly 20 mip-maps of each texture, and 12 is about the optimum number to skip to achieve a good performance to visual quality balance (I noticed that when skipping 16 mip-maps, dynamic lights that were cast on some textures would cause a strange "black line" effect - skipping 12 mip-maps, this doesn't seem to happen.)

v1.3 makes minor tweaks to the shadows, and now also includes increasing view distances as you choose a higher preset (though the differences are far less significant than the vanilla presets - the difference between Low and Ultra actually isn't that enormous). The Low and Medium presets should show increased performance over 1.2, while High and Ultra will likely not perform quite as well as 1.2 (due to increased view distance). Maximum Anisotropy passes is now also tied to the quality preset, as follows: 4x (Low), 8x (Medium),16x (High and Ultra). I still recommend trying the Medium preset first, as it is balanced for good visual quality without sacrificing too much performance.
Yes, I'm aware the cell buffers are set to 0 in this version - this didn't cause any problems on my PC, and in fact seems to help counter one nobody has found a solution for in the game (rainbow textures). While they still seem to occur at times, having the game unload old cells more aggressively can cause broken textures to be discarded and re-loaded in their proper state when the player leaves the area with broken textures and subsequently returns later (I had this happen several times during testing). There does not seem to be any noticeable performance impact to setting these variables to 0.

v1.4 is now available. All block loading distances have been standardized to multiples of 5000 as it seems to help minimize the number of objects that display broken textures after extended play. Cell buffers are now set to arbitrarily large numbers (x10 the default values) - in extended gameplay testing, I did bump into some issues I was able to trace to having zero cell buffers. The problem reported with game controllers not working with these presets has tentatively been fixed - I spotted a boolean that looked incorrectly set if one was to use one (I do not use a controller, so I can't say for sure). The Low setting is now designed to try to get the game running on a toaster - I only recommend the low preset for systems with integrated graphics, or those who REALLY want to see 60fps absolutely everywhere. The Medium preset is still the one I recommend trying first - it remains balanced for good performance without sacrificing too much visual quality. The Ultra preset has been changed to match the High preset in most respects, but has Depth of Field, Ambient Occlusion, and God Rays (volumetric lighting) enabled. If your system is able to run the Ultra preset without difficulty, you probably don't even need this tweak.