When you start the launcher, check the version number of minecraft. Choose options before launching tekkit classic, and you can see what versions of tekkit lite and Minecraft you are running. (most likely tekkit classic 3.1.2 with Minecraft 1.2.5)
It's the Minecraft vertion number that is important here, so your skinpack have to be compatible with Minecraft 1.2.5
Using a skinpack for a different vertion, may result in some mods beeing shown incorrectly and items might be shown with wrong texture (esp. in your hand when holding them)