If you see font artifact issues in the game (you'll know them when you see them), here is a solution which I learned from the Wine project forums.
Select the bottle which contains Galactic Civilizations II and select the Advanced tab. Click the "Open C Drive In Finder" button. Move all game fonts into the /windows/fonts folder. There are duplicates of some fonts, which you can delete. You will find game fonts in 3 folders: 1) the game's root, 2) within the folder DarkAvatar and 3) within the folder Twilight. The fonts to move are: ARLRDBD.TTF, BankGthd.ttf, LUCON.TTF, VERDANA.TTF, VERDANAB.TTF, VERDANAI.TTF and VERDANAZ.TTF
Select the bottle which contains Galactic Civilizations II and run Wine Configuration from the Control Panel tab. In the Wine Configuration window, select the Applications tab and highlight the Default Settings entry. Change the Windows Version selection to "Windows 98." Click the OK button.
Peform a "Simulate Reboot" on the bottle.
I have not yet thoroughly tested if this causes any new problems with the game, but it certainly fixes font legibility problems.