Most commercial wines are shipped, keeping them straight with their corks heading upwards. Although, vintage, fine, premium, good quality, and classic wines are kept flat or in a laid position where their corks remain parallel to the ground.
If you are sure about the storage conditions of your bottle of wine, then you can keep them flat while shipping or storing. But if you are not sure, you might prefer to keep them straight, so there are no chances of leakage from the bottle.