1) swimming. This is good exercise for every muscle, especially around your shoulders and arms. It is very good to burn fat and it is fun. But you will need to have a swimming pool available.
2) Running. 30 minutes is a good start to run. You can alter the intensity any time you run. You can go faster or slower, run for a longer time or shorter.
3) Interval training. I suggest to google this. But it can be applied on swimming, cycling and running. It is a great way to increase physique and performance at the same time. However, it is very demanding when done correctly.
4) workouts. With enough repetitions and rests (and drinks!) You can fill half an hour. You will feel very satisfied with the feeling you get from it. Your muscles may hurt, but it is a reminder of your hard work.
Hope this helps!