I have been researching a lot on archiving to DVD and there are may 'opinions' on the topic. A lot of people recommend against using DVDs for archival purposes and instead use flash drives and external hard drives. Working in the IT industry I would tend to disagree (my opinion) on the use of a hard drive over DVD because hard drives and flash media fail just like a DVD does. I am in the process of archiving over 2T of images to DVD now and find it to be a more cost effective solution than buying a hard drive and storing that. I found a good article on using DVDs for storage here:
This lists out the 'expected' life of a DVD. If store properly they will last a long time (probably out last me). You do need to make sure you get a reputable name brand DVD and not a cut rate provider so you know the material the DVD is made out of is of good quality.
Remember there is a difference between Archiving and Backing Up. Backing up means you have 2 or more copies of the data in different locations. Archiving is putting stuff in long term storage. For immediate work for clients always have a backup of your data that is off site. I use BackBlaze as they are unlimited on their storage. I backup 2 laptops for $100 a year ($50 per laptop) and currently have 1.5T of data protected with them. They are not an archive though as if I delete a file form my system I have 30days to restore it before they purge it from their system. I do have file versioning with them too so I can go back in time and get a previous copy of a file if needed. Think of it is a mirror copy of your live data with an option to get it back in 30 days. They do not support backing up a NAS as of the time I wrote this. It is for live data only.
I have used Mozy and Carbonite and many other cut rate providers but they do not meet my data needs. The cut rate providers that state they are unlimited are really not and others like Carbonite limit the amount of data you can backup per-day. You have to read the terms and conditions carefully. Backblaze does not limit you at all in my experience with them. I used one that was 'unlimited' until they saw how much I was backing up and capped me. Needless to say I had to threaten legal action for false advertising and they refunded me in full.
Burning to DVD is a pain but for long term archival storage I am willing to endure. We shoot weddings and events and for the older weddings they are nice to have but not necessary so they get archived. For stuff I would like to keep but not going to cry if it is lost I will archive only. For stuff I want to make sure I keep I will make 2 copies of the archive and it is now a backup. I then use LightRoom to catalog the disks so I know what is where and use key words to help fine what is there as there is a lot of data.
What I can tell you is do your research and look for reputable sources for information. Don't rely solely on other peoples opinions (like mine). Choose the method that you are comfortable with and fits your budget.