Hi Koshka,
I'm a firm believer in doing full body workouts. Split routines are fine but you can simply get more done in less time with full-body routines.
I often use weight training for weight loss as well as strengthening my muscles. One of the best exercise by far is the barbell clean and press (you can google it if you don't know how to do it.)
This exercise works every muscle in your body causing your resting metabolic rate to be higher even the next day after your workout.
I would suggest 2-30 minutes sessions per week(after your warmup), but resting only as much as you need to in between sets to catch your breath.
IT'S A MAJOR BUTT-KICKER, it helps you tone up and burn fat at the same time. Don't do the exercises on consecutive days ofcourse because resting and recovery is the most important aspect of making your workouts count.
I will admit that after a couple weeks you may get bored with the same routine no matter how effective it is, for that I usually switch in one alternate workout to break the monotony. Do a day of machine work and then get back to the routine.
It's just my suggestion, but I KNOW it works and works VERY well. The barbell clean and press is the best All-in-one, butt-kicking, no nonsense, time-effecient exercise know to man(or woman).
Give it a try for one day, give it all you got and then try to tell me your body won't change for the better after a month or more of that!
-Lee