both targa and tiff are usable by maya. PSD files can be used, but you have to use the specific PSD file texture node. And in a real application use of Maya, such as for games, film, etc, PSD file sizes are very large compared to others so it's more practical to use .tga or .tif, at least for the final.
.tga and .tif also give better image quality than .jpg. And not all .jpg images work every time with Maya, depending on their compression type.
So, it's mostly a matter of quality and consistancy.