CD-R holds around 700MB of data, and now that DVD burners have become common, is usually only used for burning music CDs. (Most players cannot handle music DVDs.) If you are copying a series of CDs (with authorization/permission, I hope), be aware that some installers will have issues if you have combined the set of CDs onto one DVD.
CD-RW used to be the primary choice for maintaining backups because you could erase and reuse it, but with most new computers having DVD burners that can burn 6x as much on a single disk, they are becoming a thing of the past.
DVD+R and DVD-R are competing formats of pretty much the same quality and price. DVD-R is more commonly supported (especially by DVD players), but DVD+R is gaining steam.
DVD+RW and DVD-RW are the rewritable (reusable) versions of the above. Not all DVD players can recognize these, so when burning movies, slideshows, etc, it may be best to stick with DVD+R and DVD-R.
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As far as speed goes, it depends. Your burner has a maximum speed, and it you insert a CD with a faster rating it will run at your drive's max speed. If you insert a slower speed, your drive will adjust and run at the lower speed. Burning disks at lower speeds typically reduces the chance of a faulty burn, but at the same time takes longer. Thus, I'd suggest getting a set of disks that can take full advantage of your drive's speed, but then use your burning software to adjust the speed at which the disks are burned, as needed. However, if you are burning DVDs to be played on a standard DVD player, remember that some are limited and cannot handle disks at faster speeds. Therefore, you should consider your audience...what is the content being burned, and where is it going to be accessed?
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Finally, more expensive disks usually result in lass chance of faults. For instance, you could go with Office Max brand DVDs and find one or two that cannot be burned or cannot be read after being burned. With more expensive brands such as Imation, TDK, and Sony, there's less of a chance it will happen, but still a chance. Thus, keep your original disks in a safe place, and if what you are burning is not something you can afford to lose (such as family photos), make sure you burn a duplicate disk, just in case.
Hope this helps,
John