I'd definitely start off with the weights first, then move over to cardio after. That way you are using up your energy to perform your lifts where you really need it. This should help you progress with your lifts a lot more. Then you should be starting you cardio with a lot less energy, which would help you to get into a fat burning state quicker.
You don't seem to be doing to much. But it's worth noting that you can burn just as much fat performing a weight program, with the added bonus of increasing muscle mass (additional muscle mass will also mean your body uses more calories in everything you do, therefore it's easier to keep the fat off). Some professional bodybuilder do not even do cardio, many do very little. the muscle mass they carry means it's easier for them to lose body fat. Also there diets are spot on, which is just as important.
If you are a beginner i suppect you're weight program revolves around machines and isolation movements. This is fine to begin with to get your body ready. Next step after this would be to learn compound moves, ie squat, deadlift, bench press, etc.
Barbell complexes are great for burning fat if you are ready for them too, they comprise are several movements put together, so for example you'd do 10 squats, 10 good mornings, 10 overhead presses, 10 bent over rows, 10 hang cleans. That is all done as 1 set with no pauses. very tough when you start upping the weights.