The most bang for your buck is HIIT - high intensity interval training. It doesn't have to be as intense as what you will see on line. For someone who is really out of shape, it can be as simple as walk for 40 seconds then sprint as fast as you can (even if that is not very fast) for 20 seconds and repeat. If you start with as few as 5-8 cycles of that, it will get you started down the right path.

As your strength and endurance grows, adding other exercises like those found here - http://hiitacademy.com/ can get you to the point of getting a very effective workout done in 20 minutes or less.

HIIT is NOT for everyone. If it is not for you, then you have to figure out your goals. Strength training done correctly will build muscle that will continue to burn fat for several hours after you are done working out and raise your overall metabolism. This will require lifting heavy. Heavy is relative, so this means heavy for you. If you can do 3 sets of 10, you need to increase the weight to really get benefit.

Cardio, done by itself, will burn calories, but won't have the same effect of overall metabolism boosting. It can frequently be done more easily because it is easier to have good form on a treadmill or bike versus lifting weights which requires some practice and instruction to get proper form to avoid injury.

One reason HIIT is so effective is it really does both. It improves strength and builds cardio and there are many of the exercises that only require your own body weight. For things like burpees, there are modifications that can be done that are less strenuous for those not ready to do the full motion. Same with push-ups and other common HIIT exercises.