Mix running in with your walking. Go for a walk. Jog part of the way. At first maybe it's just for 20-30 seconds at a time. That's ok. Steadily increase until you're running most or all of the way. (aka "wind sprints" aka fartlek)
Running shoes make a difference. They don't need to be fancy, they just need to fit! Pay attention to the wear patterns on the bottom. If the inside of the soles wear out faster than the outside or vice versa you have pronation/supination issues. Not the end of the world but it will affect your choice of shoes.
Running shoes wear out pretty fast; depending on your weight and usage they lose their cushioning after just a few hundred miles or less. My personal opinion is that folks would be generally be better off with two pairs of $50USD shoes per year vs. one pair of $100USD shoes per year -- better to have fresh cushioning than the marginal advantages of the higher end shoe. But, I am not an expert by far.
Ultimately of course, finding something fun is the key to sticking with exercise. For me it was tennis. I love playing it and it spurs me to make better health choices elsewhere in life. Though I am very much a work in progress.