I know many will perceive badminton as a "girly sport" but from personal experience it can be good for raising your fitness. I was last year at a point where I could barely manage to play 10 minutes. Now after a year I can safely say I can play 1-2 hours easily. I being a heart patient and having had 2 surgeries (requiring possibly 1 more) find this to be amazing. In fact my doctor recommends I do more aerobic excercises regularly. I cannot run for extended hours though so I find playing badminton twice a week to help me out - and its great if you struggle with sleep a two hour session can do wonders.
I would strongly recommend joing a club or playing regularly. I am fortunate that we have a club that charges £1 for 2 hours.