The ideal would be to keep your weight training completely separate from your cardio workouts.
Assign 3 days for weights and 3 days for cardio..This allows you to concentrate your faculties and energies on both kinds of workouts equally without making one suffer at the expense of the other.
But if committing 6 days to the gym is a problem then you might have to squeeze in both on the same day, again doing 1 session in the morning and 1 in the evening would be the ideal.
But even if that is not possible then it is better to do the weight training workout first then followed by cardio.The reasoning for this is that weight training requires a lot more focus on form and technique than cardio and thus should be done while faculties are fresh.
Also walking on treadmill for 10-15 min as warm up not required instead of this whole body mobility drills can be done and are more effective.
Also doing weight-training first, you can burn the majority of your glycogen stores.
Knocking out your cardio after you crush the weights will burn more fat! After a workout, your body continues to burn additional calories up to 48 hours.
This is known as excess post-exercise oxygen consumption.