Welcome .
watch the impact if your going to run on the roads a lot
Try to vary the surface you run on eg grass, tarmac, beach if possible
I've had a disc out and can pretty much carry on as normal.
Just done a half marathon !
You don't say if your a lady or gentleman in your profile but either way to improve your back strength it's a good idea to work on your stomach muscles
It's also a good thing if you don't have( there's no way of puting this politely) big guts
To help your back further posture is also important try not to slouch on the sofa or sit cross legged this puts a lot of strain on an achey back .
You 've probably been told to bend yoiur knees when you lift and to keep the weight as close to your body as possible in other words short levers .
I could go on but i'm starting to bore myself
All said and done enjoy your running
keep us informed of your progress
Take it easy
Cheriton