First off, we need to agree that the goal is not actually weight loss, it is FAT loss.
If you lose 20 pounds, and 60% of it is muscle, what's the point? Your goal is to maximize the percentage of FAT that you lose as compared to muscle.
An example...
If you manage to lose 20 pounds (down from 200) through eating less calories and doing long bouts of steady state cardio (same speed, long boring ass cardio, treadmill work, etc.), a majority of that weight will be muscle loss, around 60% on average - as shown by research.
So you feel great that you lost 20 pounds, but really only 8 pounds of it was fat. Just to compare, assume a 25% starting fat percentage (50 pounds of fat). You are now at 23.3% fat after losing 20 pounds as above.
Switch gears.
If you were to take Hippieki11er's plan, which includes resistance training (weights) and high intensity interval training (HIIT) as your cardio, that same 20 pound loss will likely be up to 90% fat. You preserve more muscle mass with this plan. (You will still lose some muscle. That much is inevitable. It's the percentage that makes all the difference.)
Back to the numbers.
Just as above you still lost 20 pounds. Congrats. But this time, you lost an extra 10 pounds of FAT, dropping your overall fat percentage from 25% down to 17.7%.
Are you more concerned that the scale says 180, or would you rather be 17.7% fat instead of 23.3% fat?
HUGE difference in the way you look.
As Hippie recommends, the ideal is to throw out the long cardio runs and concentrate on 20-30 minutes of INTENSE cardio. Combine this with 3-4 days of lifting and you will be golden.
I would prefer to see you doing the intervals on your off days from lifting, but if you have to do them same day, so intervals AFTER you lift. I think if you are pushing yourself lifting (which you need to be), you shoudl be too wiped to do HIIT after a good lifting session (especially on leg day).
Intervals can be done many different ways on many different machines.
My personal HIIT workouts look like this:
5 minute slow warm-up (walking with decent pace).
1 minute sprint (as fast as you are able to sustain for 60 secs) followed by 2 minutes of light jogging.
Repeat 3 more times.
5 minute cool-down (walking).
That is a total of 22 minutes.
If you want to change it up, try :30 second intervals with 1:30 rest periods and do 6-8 of them.
Use different machines. If outside, run between the light poles, walk a few, then run again. Same theory.
There is a plce for long boring cardio. It does help improve VO2 max, increase cardiovascular function, improve heart health, etc. So does HIIT to an extent. But you asked about weight loss (which I assume to be FAT loss), and steady state cardio is useless for fat loss.
Your lifting routine should consist of heavy loads, smaller rep ranges, and mostly compound exercises. Don't "do the machines" or spend hours doing curls. Think squats, deadlifts, lunges, bench, pulldown, rows, pullups.
It may be necessary to build some muscular endurance, which may mean reps of 15 to start, but work your way down to sets of 10, even going as low as sets of 4-6.
I love the Book of Muscle as a workout. Great, great workout with nice periodization for beginners through expert.
Write down what you lift. Don't just go in and start lifting things till you're tired. Always improve day to day. Add either reps, more weight, more sets, etc. workout to workout. And change it up after 6-8 weeks.
That's my .02
