That's not a bad idea. Swings don't agree with my back but, after reading your post, I was just looking at a couch to 5k that seems reasonable.
My fear is that I tend to have trouble keeping up with pre-written programs. They always progress faster than I can keep up and I end up feeling beat up and frustrated. But I suppose there's no reason I can't make adjustments if necessary.
All programs require some adjustments in order for you to keep making progress.
However C25K seems to work very well. People who are old, obese and never trained in their lives seem to have success with it.
And it pretty much starts off with run walks. A lot of run walking. So imagine running for 30 seconds and then walking for a few minutes. Repeating that a bunch of time with distance slowly growing.
Swings can be a lot to begin with. Especially those with a glass back. My wife's lower back gets incredibly tight and sore from very little working sets. She likes the tactical barbell approach of 1 working set of deadlifts per week. She is also a strong squatter and likes to squat 3 times a week.
However she likes S&S. She started off with a really light bell and built up very slowly over time. 12kg IIRC.
No reasoned why you couldn't do the same. Start off with an 8 kg bell and build up VERY slowly over time. Putting more focus on the C25K program and using S&S as an accessory. Therefore not as important as C25K. It is there to enhance your results.
A couple of things to bare in mind.
- Stretching your hamstrings, hip flexors, calves and tibs post run and whenever these areas are feeling tight during the day. Very important for preventing injury.
- Stay hydrated, drink plenty of water and salt all of your meals.
- Run slowly for all of the running portions of your program.
I won't bombard you with foot strike or anything like that. Right now it is more important to get you on the path to being active.