Hi hoopman!
I have Degenerative Disk Disease too and I’m only 19. I understand the frustration over stiffness and pain and yes, sitting at a desk all day is sure to aggravate it (which I do because of school). My spine is also stiff and some days I feel like my lower back is going to give out on me. I don’t know if you get any sciatic nerve pain due to your compacted disks or not, but I can tell you from personal experience that yoga is 100% the way to go if you have DDD and any resulting nerve pain. It helps with pain, stiffness,and relaxing all those muscles that have tensed when trying to “protect” the injury (aka those bad disks). I have tried physical therapy, electrode stimulation, ad other things but yoga is the only thing that gives me any relief. If you strain too hard though or try to do intense poses that push your limits, you will hurt more. You need to honor what is right for your body.
As for preventing further degeneration, the doctor told me that degeneration in general could get worse overtime or it may stay the same. There is no way to fully stop degeneration, as it is part of the natural aging process, however, yoga can help relieve the pressure on your back unlike other activities like running which the doctors advise against.
To make a long answer longer, I think yoga is a great choice for you!
Some helpful poses:
pigeon- for sciatic nerve pain related to back injury
cat/crows- for that thoracic stiffness
butterfly (laying on your back)
low cobra
Good luck!