Walking stairs while carrying a weight. Notice I said "walking", not running. If you carry even a 25 pound weight, walking up and down will have your heart beating out of your chest! I find a plate is better than dumbbells, as it puts less stress on your joints. I carry it behind my head most of the time, but flip it down and carry it on my chest for a break too. This is essentially what TahoeBackPacker likes doing on his hikes, but this is something I can do even when weather does not permit. I also find making myself hold the weight, rather than using the vest, keeps my joints strong too.
I've had a lot of success with spinning/cycle classes, say 2 - 3 times a week. They are also good for building your core if you hold the proper position when you are out of the saddle and don't hold up your body weight using your hands on the handles. My core has gotten a lot strong through cycling (indoor and outdoor).
two ways to run on a treadmill. 3% incline for an hour. 250 calories burned. Congratulations, you're a gym tourist. Not an effective use of time if your goal is to lose weight. Crank the incline up to max. you slow down. But, you can make that red LED guestimate meter read 800-1000 calories after an hour. That incline activates your quads, glutes, and calves increases your cardio effort. Start leg strength development as soon as possible as this helps you maintain that level of effort longer.
Another machine to check out is the Precor AMT100i Adaptive Motion trainer.
I can kick my own ass in less time on a machine like that. But, with a retail cost of $8,000, you may have to search for a gym that has a few of them.
I strongly recommend that you keep an eye on your heartrate using the built-in heartrate receivers Precor and StarTrac build into their control panel. The most popular brand they support is Polar.