Did some experiments with metal detecting many years ago, and found that the two coil T/R induction type is best for general use. It's relatively easy to discriminate between iron and nonferrous metals, but discriminating between nonferrous metals is hard as there is essentially no difference in the magnetic effects of aluminium or precious metals. Gold or silver gives a stronger signal per mass because of its better conductivity, but then a drinks can is larger than a ring or coin so that cancels out. Interestingly I did find that cupronickel allow such as some UK coins are made of could be identified by its magnetic reluctance, albeit only at close range.
I can't imagine a ferrite rod would be any use except for very short range, the larger the diameter of air-cored coil you can manage, the better the depth penetration.