No, any corked beverage should be stored on it's side. Think about wine racks and such, all have the bottles sideways. But for your purposes, whatever you buy will probably be used right away so I wouldn't worry too much about it.
Once opened, you can store it right side up, but wine does not last for more then a few days open, some wines mature then go over within 24 hours, tasting like vinegar and becoming really sour. I only open my nice wine ($80+) if I am sure it will get drank. If I'm not sure I'll open the cheap stuff, and whatever does not get drank that evening gets dumped. We have a chain in CA called BevMo that's a big liquor store, they have these sales, buy one get one for $.05 so I try and go stock up a healthy mix of good/cheap. Best. Sale. ever.