Talking from personal experience:
Beware of the slow jog / fast walk routine. It will conceal your real progress because you will have to go through a long period where your average speed doesn’t increase much, or perhaps even gets slower.
As you improve, you can do more of the slow jogging and less of the fast walking and still maintain your heart rate. However, if your jogging is only a bit faster than your walking, your average speed will only increase slightly. If your jogging speed and walking speed is equal, your average speed will not increase at all.
And if you are in the situation that I was in – that my slow jogging was slower than my walking – then your average speed will actually get slower as you improve.
I solved this by forcing myself to jog really, really slow. I had to start at 4 km/h (15 minutes/km or 24 minutes/mile), which was only 2/3 of my walking speed.
I have absolutely no idea whether this was a good idea from a training perspective. But
from a purely motivational perspective it felt terrific. I could see my jogging speed increasing slowly and steadily over the months, which made me confident that I was on the right track.
(Well, slowly and steadily is not entirely true. The progress came in “lumps”, interspersed with weeks of stagnation.)