Mumiah: Hold yer horses right there! Gamma-adjustments shouldn't be adjusted unless you really know you need it (or unless funky old games like Riven commands you to), but anisotropic filtering (AF) and anti-aliasing (AA) is definitely something you'll have interest in working with. If you don't remember what the gamma was set to before you changed it, see if you can find some 'Reset'-button - or if you're satisfied with your present gamma-level, just don't worry about it. It only changes monitor brightness, more or less.
Now, to AA/AF. AA affects the contours of the 3D-models (through various possibly ingenious ways), BUT it will make demands on your GPU - loads of calculations needing quite a few core-MHz. Depending on what you set the FF8 Launcher to, and your monitor-size, you might not actually notice a difference between 2x and 4x - never mind 6x and 12x - but your GPU definitely will. If you notice lacking performance, AA is the option you should reduce first and see if it helps.
AF takes samples of the textures and scales them to... well, different resolutions, I'm not sure about the inner magickery of that. Now, this will take HUGE chunks of your VRAM. If this were a somewhat new game with 4092x4092-textures... Don't. But, well, as FF8 probably predates 1024x1024-textures, it should be safe to set the AF-multiplier to just about anything you like. You just most likely won't notice a difference.
The affected parts are textures on 3D-models, either placed at an odd viewing-angle or far in the distance. In other words, you MIGHT notice it A LITTLE in the combat-screens, and you'll notice it more on the world map, but NOT AT ALL in field-maps (cities, Garden, 2D-backgrounds, those tings).
(Actually: In older games - and FF8 before FF8 Launcher - AF has a tendency to cause really interesting effects. I don't remember what causes the grid-artifacts in FF8 (7 too?), but it definitely did something in FreeFalcon 3/Falcon 4 while in 2D-cockpit view.)