I think when you're just starting out with a workout program, the timing doesn't really matter that much. You should do it at a time that's convenient for you and when it will be least unpleasant to work out. So, for me, I'm not a morning person at all so when I first started working out, I always did it in the evening or even late at night because that's when I felt most energetic and most likely to want to work out. If I had forced myself to do it in the morning, I never would have stuck to it because it would have been torture.
So when you run really depends on when you're most likely to want to do it. You could also switch it up. If you want to do stuff after work one day, run in the morning. If you want to sleep in on another day, then run in the evening.
If you're hungry after work, then you should either run after dinner or have a snack before your run. Working out hungry when you're just starting out is also not a good idea because it will make it more unpleasant. I think, at this point, the most important thing is to do whatever it takes to make the experience pleasant so that you'll stick to it. Tweaks to optimize performance, fat burning, or whatever can be added later if you want.
Not sure if you like audiobooks, but the thing that really got me into working out is listening to audiobooks. I listened to music at first, just like everyone else in the world, but it just didn't do it for me. It didn't distract me enough. Once I started listening to audiobooks (fiction, mostly), I looked forward to my workouts cuz I get to find out what happens next in the book.