I started slow jogging every other day, using an app called Just Run that has you alternate walking/running until you're built up to running a full 3k. It goes for 9 weeks and I just completed week 6. There's a 10k version I'll be moving on to after.
On the days I don't run, I use Chloe Ting weight-training videos on YouTube to target areas I need strength support in, like my lower back and shoulders. I also use her cool down routine every day, it's the best stretching video I've found.
I've also been fasting every Monday. Just nothing but coffee (which I do put some sweetener and milk in in the morning) and water.
I only weigh myself once my period has come and gone, since I tend to fluctuate about 10 lbs during. I weighed myself about 3 weeks ago and I've lost 13 lbs. I've just now started seeing and feeling a change.
Running for half an hour burns about 400 calories. 1 hour of running, 800. 3 runs a week can burn a day's worth of calories. Don't understate the impact exercise has.
While exercise will have some impact the vast majority of weight is controlled by what you eat not what you do. Also calories are not burnt in a simple one to one equation. Different types of calories are processed definitely in the body. Sugar turns to fat, but the same amount of calories in bacon, or carrots, or bread, are all different, and your body will use them differently. The less processed a food is, the harder it is for your body to extract those calories, so measuring calories from what it says on yh packet is not the best guide.
Definitely do both if you need to, but don't under estimate exercise. I went from 10.5st to 9.5st just doing couch to 5km and then continuing to run 5km 3 times a week, no other dietary changes.