Get Strong First
It seems to me like a lot of people are confused about what a barbell is used for. You lift to get strong, not to get in shape. Conditioning is much more effectively built with other activities. You do not need to do a bunch of circus acts with light weights to get in shape. You lift to get strong, plain and simple, and you should definitely get strong. I have discussed why many times, just remember that strength is the foundation of our physical performance. Everything we do is dependent on strength.
You get stronger by lifting heavier weights. That is why we add a few pounds to the bar each workout. Little jumps eventually add up to large gains. Strength training requires focus, consistency, proper execution, and rest in between sets for recovery. Heavy training (which is required for building strength) requires sets of 5 reps followed by a few minutes rest between each set. This is how strength is built, and again we lift weights to get strong.
Once you are strong and your goal shifts to getting in shape you need to find appropriate conditioning to do after your strength work or on your off day. If you need to lose a few pounds it is best to add in a combination of low-intensity/low-impact conditioning and high intensity/short duration interval training. In my experience the low-intensity/low-impact stuff is important for heavier people who have more fat to lose. Obviously, any conditioning program should be supported with a sensible diet plan if fat loss is the ultimate goal. If fat loss is not much a goal for you than 15-20 minutes of high-intensity interval training once or twice a week will get you in good shape.
Athletes who are involved in sports that require higher levels of conditioning like hockey, basketball, tennis, or wrestling probably need to do a little more work. However, it is important to keep in mind the importance of strength and to be sure the athlete is not unnecessarily weakened from over-conditioning.
Getting started on adding conditioning is much like getting started training for strength. Establish a baseline starting point. Be conservative. Get started doing less than you think you should. Each conditioning session add a little. You can add minutes, reps, intervals, intensity, distance, etc, but don't add them all in the same workout. Slow and steady always wins the training race.
Regardless of your training goals. Always take time to build a foundation of strength. Then once you have ran a linear progression focus on getting in shape. Getting in shape involves developing an appropriate level of conditioning and losing excess body weight. Get strong and then worry about getting in shape.