first off, you should ALWAYS lift weights first.
second, 15 mins isn't enough weight training to be worthwhile.
third, I'd split up your routine and do weights 3x a week, cardio 3x a week, alternating them.
saying that fat burning doesn't start until 40 mins into cardio is too general a statement to be true.
The body can burn fat as long as its aerobic exercise. But you need to increase muscle mass with weights, because muscle burns calories. if you diet and exercise yourself into looking like a toothpick, you'll have to eat less than a hamster to maintain that weight.
if you put on muscle, and shed some fat, you'll be able to eat more, because you'll have to eat just to maintain the muscle mass, in addition to eating for energy to get you through daily activities.
45mins of cardio is god's plenty. 20mins of intense, interval style cardio is even sufficient, but it does vary from person to person, as well as beign dependent on your goals and your current level of fitness.
20 mins of intense cardio affects a morbidly obese person far more than an athlete. your magic cardio interval might be 25mins.
If you were doing 45 mins, that's slow, steady state cardio, and that kind is best done first thing in the morning on an empty stomach. A 3 mile brisk walk would qualify...even a few little sprints or jogging a couple blocks in the middle.
for evening cardio, 20-30 mins of higher intensity cardio, or intervals of varying intensity is a better system.