Any modern DVD player will read all forms of blank DVD as well as play back JPG photos and MP3 music stored on a DVD. This includes your basic $30-40 models. Some older ones would read -R but not +R, but those are very rare - generally, they'd read nothing or both. You'll probably find more difference in older players being picky about the brand of media and how fast it's burnt than if it's -R or +R.
There is nothing special about a CD or DVD itself that make it different, they are just places to store data. There are special formats for CD audio, DVD video, etc, but the discs themselves are just data storage. In other words, whatever you used to burn a CD of data should work for making a DVD of data - except that a DVD will hold ~7 times as much data.
I'm not too concerned about "archival" media as I'm sure that I'll be re-burning my good stuff before long, when BluRay burners and media (which holds about as much as 7-8 DVDs!) becomes cheap. After that, another format will probably come along.
I also have many CDs that I burnt over 10 years ago and very, very few have errors. They certainly can go bad over time but I think most of the talk is just FUD created by the companies to sell you expensive archival media.
Once your pictures have been backed up (ideally to two DVDs - they're dirt cheap, after all!), you can leave them on your PC as long as you have a good amount of free hard drive space. If you're not running out, there is no reason to delete them - it won't make your PC run any faster or slower.