It might depend on the engine, and this info might be a few years old now (and might not be 100% accurate) :
DDS - small size on disc, small size in memory
PNG - small size on disc, normal size in memory
TGA - large size on disc, normal size in memory
JPG - small size on disc, large size in memory, no alpha channel
BMP - large size on disc, normal size in memory, no alpha channel
I can't remember any specific numbers though - but something about graphics cards could read DDS without needing to uncompress it, which meant it used a lot less memory in game.
Within DDS :
DXT1 - alpha on /off (100% or 0% solid - can't have 50% or any other number)
DXT3 - alpha variable (100 - 0% solid - i.e. 50% here, 30% there is okay)
DXT5 - alpha variable (100 - 0% solid - i.e. 50% here, 30% there is okay)
I can't remember the difference between dxt3 and dxt5, or if there are other (or newer) dxt numbers available.
[edit] In pistacja's link above, it shows dxt5 has a smoother alpha
I don't know if you'll need alpha channels, or if the engine supports it even. Could it be useful for death animations (i.e. a hole shot in the chest), or having a damaged / blood layer on the models to show injury?