In my personal experience I've found strength training better for losing weight than just cardio but any activity will help a bit. You'll really need to adjust your diet in some way for it though, or at least start counting and keep your calories steady as you do more activity. Trying to outburn what you eat takes like an hour of exercise a day otherwise, it's tough.
The problem with doing a lot of cardio is that you need muscle to burn calories (especially so without injury and as you get older), and too much medium intensity cardio will start to chew up lean mass.
No harm in doing a bit of both though, especially if your goal is fitness/maintenance rather than maximum strength or a particular look.
Tabata (the sprint/recover running technique) was developed, I believe, to increase VO2-max. It should help with overall endurance, and you can go on a long run each week. That would probably be efficient.
I guess the answer for optimizing time is to get a home treadmill if removing the commute to a trail/track will make the timing work.