Well... this could be a very complicated discussion, but also as simple as it gets.
Will a mile + tempos help you to burn fat? Damn sure yes.
Is it optimal for fat loss? Probably not.
According to the book, the best fat burning thing to do is low impact steady state cardio. Jogging for 45 minutes, really relaxed, almost at fast walking speed, keeping heart rate at around 120bpm. But since we are jump people and basketball people, mixing a few more elements helps. This thing i do is a good mix of all. A fast but not all out mile run improves aerobic endurance without pushing lactic threshold, while tempos improve anaerobic endurance. Plus the added stimulus ( RFD, ankle stiffness etc ) from the sprints. Plus it is sooooo less boring than steady state cardio. Plus a good deal at the calories burned repository ( not most fat, but not all glycogen either ).
Since you are not used to running & sprinting much, together with your distance fears, i would say ease into it.
Start with the 'long' run as warmup. For starters fuck distance, just jog in a moderate pace for 15 minutes.
Then rest 5 minutes.
Then go for tempos, say 3 sets of 5 reps 100m. Start at 50% , so 100m should be around 20-25s. Run the 100m, rest 1 min, repeat. 3-5 minutes between sets.
Then instead of the jumps that i do, you can do a cooldown run, like the starting one but slower. Or jump. Or some plyos. Whatever.
Then you can start progressing it. Establish a standard distance for the first part ( the run ) , like i have established the mile, and start pushing your speed a bit more each time. Same with tempos, when you feel you can do the 3x5@50% with 'good breaths', bump it up to 60% and so on.
But in general, don't get too caught into fat loss details, whatever you do will work as long as you do it. Go out and do whatever running thing comes to your head for 45-60 minutes. Steady pace running, fast walking, tempos, sprints, basketball shooting around, a little bit of all, they all work.