While some will argue DVD+R is best for storage and DVD-R is best for movies, the actually differences are negligible. Both are just as adequate for either task, and will last the same length of time. How long that time is, though, depends on the media itself. Unlike bought DVDs, recordable media doesn't last a lifetime and depends greatly on the storage conditions (temperature, humidity, use of labels, etc) as well as the original quality itself. Some will fail out of the box while others will last 20+ years.

The best advice is to purchase reputable brands, store in a clean, cool, dry, dark climate, and don't use sticky labels or write on them. (The ink/dye/glue can actually eat through the DVD's thin metallic layer over time.) Pull them out every few months and randomly try opening files, and burn a new set of DVDs every once in a while. Keeping two sets of DVDs isn't a bad idea if it's truly irreplaceable data.

As to the problems you encountered, it could have been a bad batch of DVDs or it could be the drive...when a multiformat drive goes bad it may have problems reading/writing a particular format.

Hope this helps,

P.S. Keep in mind that not all DVD drives and DVD players can handle both formats, so if you're going to share files or home videos check what the other person's drive can handle first.