It clearly depends on the protein stability, some are fine at 4°C some at -20°C and some at -80°C I recommend to put glycerol 10 or 20% final concentration all time. Some proteins are stabilized by ammonium sulfate and at 4°C but to me: Minus 80°c and 10 % glycerol are very often good and you can keep for months... Do aliquots to avoid freeze thawing cycles that are always bad. If it is an enzyme sometimes addition of substrate helps storage for long term.
There is no universally good protocol for protein storage, it depends on the specific protein you are working with. Your best bet is to scour the literature (if that protein has been purified before) to see what others in your situation have done before; failing that, Brigitte's advice above is excellent.
Alejandro is right in his statement. Long term storage depends on protein nature. In my experience, metallo proteins are more stable at 4 degree Celsius (up to months) than non metallo proteins. It also depends on the kind of buffer system is being used. You need to explore much about the nature of your protein through literature.