Answering this needs the intended duration, since a fortnight and two years call for different arrangements.
Lyophilised powder: refrigerated at two to eight degrees for months, frozen at minus twenty for longer. The gain from minus eighty over minus twenty is small for a dry solid and is not usually worth the arrangement.
Position matters less than people think: upright or on its side makes no difference to a lyophilised powder, and upright is marginally better for a reconstituted vial because it keeps the stopper dry.
The 28-day in-use period for preservative-containing multi-dose preparations is printed on the diluent labelling and is a long-standing pharmacy convention.
Nothing here is medical advice, and research-use compounds are not approved for human use.
Label the vial at reconstitution with date, concentration and units per dose.