I've used the 'tuff rib' type metal roofing. People just call it Ag(ricultural) Panels here. It's 36" wide and you screw through it. Lots of people will say it's garbage and leaks, but I haven't had a problem.
The proper screw location is supposed to be through the flat span of the metal, but I've listened to the other half of installers that insist (logically to me) that it should go through the raised ribs. The roof will never leak if the screws go through the ribs, but they might fatigue and could fail after some (10, 20, ??) years. The easy solution is to just replace the screws if that happens.
I replaced my old metal roof with ag panels when we renovated 10 years ago. The original was called '5V' style, in which lead capped nails were pounded through the raised V ribs. The 65 year old roof didn't have any leaks, even though 10% of the nails were missing completely, and half had backed out significantly or lost their caps. The 1x6 purlins underneath were in perfect shape.
I would not install a metal roof on top of existing shingles. I have seen some houses done like that-- in particular, the one we live in now. The previous owner had it installed just before putting on the market. The contractor lays roofing paper on top of the shingles, and then fastens the metal roof directly to that. Horrible idea, particularly if the screws go through the flat section of the panel. The screws don't seat properly since the underlying surface is wavy and there are many screws with gaps from day one. This is because if the screws are tightened completely, then the ripples of the shingles will show through, so instead, they just barely make contact.