Honestly in my personal experience weight loss is like 90% diet. It simply is much easier to eat less compared to how much it takes to burn those consumed calories. General fitness and feeling better through that is imo more where exercise comes into play. So I'll split my answer into two parts.
Building sustainable habits is how you achieve your goal
1kg of fat is around 7700 calories. There are a ton of different diets and ways to lose weight. It's probably very subjective which ones work best for a person. But in the end they all come down to reducing consumed calories.
For me it was basically easiest to adjust the further away from eating the change happened. So adjusting what/how much I buy. And then the portion sizes being cooked. Once it's actually on the table/plate it becomes much harder for me.
But others might be different and intermittent fasting or something completely different will work.
As far as exercise goes again the best one is the one you enjoy and thus actually stick with doing regularly.
For stamina I ended up with running (stared with the couch to 5k program), but others might prefer something like cycling.
For strength just having a pair of dumbbells laying around (later added a bench) got me started since I preferred that over other types of exercise. There are plenty of basic routines e.g. on YouTube. I don't really think especially which one you pick as long as you start.