A lot of people propose cardio here, but I will take a different route and recommend strength training. Compared to the former it has the following advantages:
Improved posture and strength: When you get stronger sitting, walking and standing with good posture will become a lot easier, will feel more natural and you will start to do it without constantly reminding yourself. Other common task like house holding or carrying objects will get a lot easier as well.
Permanent fat loss: Strength training will increase muscle. And one of the benefits of increased muscle is an increase in the number of calories your body naturally burns at rest. In addition to this your body will burn calories during the weight lifting session and will require additional calories to repair your muscles after it. These three effects in combination work really well: When I started to lift weights I became a lot stronger and leaner within a few months without changing my diet habits at all.
Less time consuming: 3 x 45 minutes per a week is enough.
Increased motivation: Pure cardio tends to be boring and repetitive. If you take strength training seriously you will try to lift more weight, perfect your technique and try to break your own records every workout (and if you just started to lift weights, you will most likely break them every workout). If you are a gamer, you probably know this kind of motivation from RPGs, where your character get stronger from level to level.
Various other benefits: Strength training increases endurance, bone density and testosterone levels. It also strengthens your joints, lowers cholesterol and improves your sleep.
It will make you look good: Strength training will not only make you leaner, it will add muscles to your body as well. You won’t become a body builder or anything close to that. You will look athletic and in shape.
If you want to start with strength training, I recommend you to read Stronglifts as an introduction. It is a great site that will offer you everything you need as beginner: Workout programs, articles about exercise technique and nutrition advice.