My gym trainers were split on this one.
I definitely agree that warmups are essential when doing weight lifting. However, I also believe that warm up sets of the same weight exercise are a better way to do it. I'm more motivated to warm up by doing 40% to 50% of my usual weights in two high-rep sets, than I am to to some general stretching and warming exercises.
I also have had no more re-occurences of mild joint\tendon injuries after I started doing warm up sets combined with weight-acclimation sets.
Some theorize that weight lifting first brings you closer to the fat burning stage, making your subsequent cardio session more effective. Even though weight-lifting is anaerobic, is still burns glycogen after all. Other camps (the Max OT camp, which I don't agree with 100% either) actually say that you should space cardio 8 hours apart from weight-lifting, or you could overwork your muscles and end up burning through any muscle gains you might have had.
What I have tested is doing cardio in the mornings, before a meal and with adequate hydration. Your glycogen levels are naturally lower than any other time of day and the theory goes that you enter the fat burning cycle much sooner. This means that your morning cardio is more effective at burning fat, for the same amount of time and effort. I definitely noticed quicker results with my morning cardio compared to when I did it evenings.
Again, these are all theories -- but morning cardio, or cardio after weight-lifting is what seemed to be optimal for me.
Don't be afraid to try out different things, listen to your body, and good luck!
ETA: You know, trying to answer questions like this is actually good for me because I often end up putting my foot in my mouth and discovering that what I took for granted is actually wrong. In this case, I'm half-and-half. According to
this article,
a) morning cardio
does not make a significant difference, and carries a slight risk of burning more muscle,
b) cardio before weights is good if you're aiming for endurance training, otherwise cardio after weights will burn more fat,
c) cardio on non-weight days really is optimal, if you have the time to do it.