What are the different item quality characters

If you want to use the tileset in fullscreen mode, locate and modify the [FULLSCREENX:800], [FULLSCREENY:600], and [FULLFONT:curses_800x600.bmp] configuration lines to match the specifications from the tileset list. The FULLFONT directive should match the filename of the tileset you downloaded. If you want to use the tileset in windowed mode, search for the [WINDOWEDX:640], [WINDOWEDY:300], and [FONT:curses_640x300.bmp] lines instead, and change them to the correct values.

Source: http://df.magmawiki.com/index.php/DF2010:Tilesets

The 800 and 600 values are dependent on the size of your new graphics and the size of your screen. A tileset with 16x16 tiles will be 256x256 pixels large, and the target resolution will be 1280x400, unless you change the tile width and tile height in the same file.

I believe that core quality refers to the item itself - i.e., a superior-crafted door, and total quality takes into account the masterfully encrusted with blue diamonds and other miscellanea.

I've been using "Core Quality" for a furniture stockpile of masterwork doors (admittedly, in 31.16) and only masterwork doors are going to that pile.