Rosieglow - the discs are different formats. Some DVD drives can write to both formats, while others can only write to certain types.
DVD-RW was developed by Pioneer
DVD+RW was developed by The DVD+RW Alliance.
For backup purposes, you may wish to buy DVD+R or DVD-R discs - they can be cheaper, and are NOT Rewritable, meaning that you can't erase your photos. They are typically a Write Once medium... so you need to collect your photos together, then write them to the disc in one go.
Flocci... I've not experimented with writing video to a DVD disc, for playback on a standalone DVD player. You may need to experiment a bit with software to get that working perfectly.
Nero software I think is quite popular, often bundled with drives. 15-day Trial version (185MB)
Xillisoft DVD Creator is a lower cost option.
ImToo DVD Creator is another, with a free trial version - so you can try before you buy.
Fox DVD Creator has a 30 day trial.
I would suggest downloading one of the trial versions, and seeing if it works, before parting with your money.