Anyway, it should be faster thant the structural relaxation of the melt. In the case of metals it must be very high (more than thousands of K/sec), in the case of silicate glass or polymer glass it can be signficantly slower. The faster the cooling the farther you are from equilbirium. If the melt viscosity is high, the structural relaxation (physical aging) in glassy state will be low. In the case of low molecular glasses or metals it may happen that annealing results in crystallization.
The answer from Gyorgy is correct, I would like just add a couple of words about the water case.
As you maybe know, also water can be supercooled and also made in glass state. To reach the glass the cooling rate must be faster than nucleation. For water this means about 10^6 K/ sec.
you may also consult the Rawson criterion in order to assess the trend for glass forming: the higher this Rawson value, the lower will be the necessary cooling velocity. I hereby send you a document which could be of your interest. Regards
Actualy there is not a best cooling rate. It is better to refer to a CRITICAL COOLING RATE (Rc) at which you obtain for example 1ppm of crystalline phase on cooling.
Below Rc you get a larger crystalline phase fraction.
Above Rc you get a lower crystalline phase fraction.
Rc has a different value for each chemical system. For example very low for SiO2 (about 0.001 K/s ) and very high for metals (about 10000000000 K/s)