Don't use TGA. PNG files are smaller, and they will thumbnail in Windows.
DDS is great, because you can auto generate mipmaps. But it's a pain trying to find plugins to enable open/save of DDS files for most graphics editors. Gimp is a good choice.
Also DDS doesn't thumbnail in windows. So it's a pain opening a directory full of images and trying to get a good sense of whats really there.
DDS is the best for a game.
PNG is the easiest to work with.
Edit: Also save original non-flattened versions of textures (master copies) as PSD documents.