Which singing lessons shall I start?

All genres have similar techniques at the core. In the end, it's the shaping of the vocal tract and vowel choice that are the main differences (and a few other things). But seriously, when have you seen an opera singer use distortion techniques? Some techniques are not used in certain genres. Anyways, you learn any style from a good qualified instructor, you'll learn vowel modifications, Bridging registers, tuning formants (the reason why you think opera singers don't use other registers, however, most people desire to do this whether or not they know what it is or not. Sometimes known as "blending"), resonant placement, proper breathing techniques etc. all styles demand these to some extent. You should know that SLS is a faulty method to learn from. CVT is a great method with lots of scientific research behind it, but it's only effective if you learn from a CVT certified instructor. These are known as methodologies or pedagogies. The best approach is to find a qualified instructor who knows about the physics of sound as applied to the human voice and laryngeal biomechanics. I will say, though, it may be possible that you need to go to different instructors to learn a specialized technique to a certain genre such as distortion. Rock instructors will teach this, but classical instructors won't (however, I have heard of some classical instructors open enough to modern techniques that actually teach it)