Writing this since nobody really seems to have written anything much on them, aside from the XIwiki page which isn't that detailed.
Bump Mapping.
This only works on zone textures, nothing else.
In theory this should be good, it's supposed to add extra raised and recessed areas to flat textures. Basic example below.

It's implemented poorly in FFXI.
The way it seems to work here is that when you activate it, a new invisible light source is turned on and depending on the time of day it adds highlights and depression effects to certain areas depending where the sun is supposed to be.
So for instance if you goto Mhaura or Rabao in the morning or evening you can see wave effects in the sand (to signify the low sun causing mini shadows on sand curves) and more definition on the cliff walls during the mid day.
The problems with it are that:
The effect looks different based on the time of day, the light effect is too white and harsh (almost looks like frost), it won't work with many HD mods since many modders don't update bump maps, it's broken on some maps (quifim for example you can see seam lines when using bump mapping), it uses more system resources.
Personally think it's best turned off.
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Mip Mapping
Mip Mapping basically reduces shimmer, it creates smaller versions of all the textures you come across on the fly to swap to as you move away from objects.
This is good most of the time, however with some big mods it can lead to hitching issues when you come across new stuff, as the game creates these mipmaps on the fly. Impact probably depends on the strength of your hardware.
Since I use some mods I have this around the mid point, if you use more you want it lower and if you have none you can set it as high as you want.
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Texture Compression
This is purely for skybox textures, clouds, some light glows etc. If you put it on high it makes a big difference (test it in starter cities), however it's still disabled in some zones and ignores the setting (meri mountains skybox for example).
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In-game settings:
Menu > config > Misc:
Shadows off / normal / high. Shadows on players: low = blob shadow, medium = HQ shadows, high = will show HQ shadows and will add things such as extra shadows when mounted. These can cause performance issues in busy areas obviously.
Weather Effects -On / Off- This basically just removes cloud effects, sandstorms, rain etc.
Character Models Displayed:25 > 50 character models displayed around you. In theory good, in practice bad. Can be good for alt accounts.
PC Armor Display: This is either normal or static, static means everyone else will appear to be wearing level 1 gear at all times around you (if they are already displayed you have to zone or move out of range of them for it to change). This means the game doesn't have to load all that gear, it won't be changing it all the time. Can make a big difference in stuff like DynaD if you're having lag problems but remember to set it before you enter.
Menu > config > Misc 2:
Clipping plane: This lowers the distance the scenery loads, more fog basically. This can have a noticeable impact on performance if you go extreme with it, especially if multi box.
Menu > config > Misc3:
Weapon Effect: This is things like Ambuscade animated weapon effects such as the lightning. Almost no impact on performance, more a visual thing. Does not work on REMA glow.
Menu > config > Effects:
This can have a massive effect on performance issues in stuff like DI and DynaD, can disable all graphical effects from spells, ws etc In stuff like DI (where blaze spikes can destroy your fps) it can take a 5fps fight to 30+fps+