Going to have to say if you want to condition to properly perform a workout such as described above with sprints, you'll need to do some long runs because to do a proper speed workout you'll need a base of endurance to actually benefit and improve, and you should not being doing anymore that three speed workouts a week. If you do workouts like that everyday, either you will get injured, you will very easily plateau, and you just won't get very far.
In any good speed workout you never stop, for a starter workout after at least 3-4 weeks of decent mileage. A very easy workout, warmup with a couple miles, then get on the track and sprint the straights and a very slow jog on the turns. That would be around a 120m for each sprint the first time i would feel out what your capable of before you push yourself. This is only need so your body gets used to the transitions in speed and adapts to these kinds of workouts, starting with something like this is asking for trouble, most likely without experience you'll make it about two laps if using a track, not being able to gauge your distance capabilities.
Then after you've done that for a couple weeks move into 400m sprints, with 200m rest, then past that 800m sprints with 400m rest. If you get there you can move up to 800m with 200m rest, 1200m 600m rest and continue alternating, your rest should be a very very slow jog so you can gauge your recovery, but its up to you if your allowing yourself to recover or just taking it easy. The reason you shouldn't start with these is because you will not be able to commit to the properly with out a solid foundation with distance.
After a sprint the dumbest thing you can do is just stop, and stand or sit, or bend down and grab your knee's your only making it harder on yourself and your body, or if you use a treadmill never support yourself with your hands it just lazy and done by people who don't belong on a treadmill.