Skinny fat, busy schedule, thinking about running — need advice

I want some advice regarding my situation.

24 years old male
5.8 ft
69–71 kg bodyweight

Skinny fat. No workout currently and I don’t really have the intention to go to a gym.

I used to be in better shape before.

My schedule is the main issue. I work 6 days a week and with commute, I’m out around 12 hours a day. After coming back I still need to cook and study, so most days are quite packed.

Weekdays I might only manage maybe 10–15 minutes if I try. Sunday morning is the only time I properly have free.

Another thing: I fast on Mondays and Thursdays. My diet is also pretty bad right now, not very structured.

My goal is simple: just get back into shape and lose the skinny-fat look.

So what would you focus on first in my situation?

Diet?
Short bodyweight workouts?
Running / walking/jump rope?

I’m actually pretty bad at running but I'm open to improving overall.

Also one more question: should I get a fitness tracker/wrist band or something like that to stay consistent?

Just looking for practical advice from people who had a similar schedule.