In the long term, it’s best to store your wine bottles horizontally. Like any other wood, cork will expand when damp and shrink when dry, allowing air leaks and spoilage. Storing your bottles horizontally keeps the wine in contact with the cork, maintaining the correct size and keeping your wine properly sealed.
The air leaks are very slow, so if you plan on drinking the wine in the next few weeks, of course, there’s no harm in storing these bottles upright. It’s those age-worthy reds and longer-term whites that need special storage treatment.