As a trainer, I suggest my clients warm up on any piece of cardio equipment for 5-10 minutes, then weight train (again first set on the light side to prepare joints and muscles), then stretch following weights. Cardio last for same reason as previous post stated...don't want to enter weight training tired as form may suffer.
I'm a big fan of doing short (20-30 minutes), intense interval training on an empty stomach to burn fat, preferably first thing in the morning. If someone were diabetic, though, I'd tell them to follow their MDs directions. I don't think high intensity interval training is appropriate for anyone who has been sedentary for years though. In those cases, I suggest steady state cardio reaching your target heart rate for 30-45 minutes (work up to it as first couple of minutes should be on the easy side). Heart rate monitors with the strap around chest are good tools to monitor your heart rate and are much more reliable than the monitors on the cardio machines at gyms. If you don't have a hr monitor, you can use your own perceived rate of exertion. Basically, this is based on a scale of 1 - 10, 1 being you're laying in bed and 10 being you're about to hyperventilate. Want to aim for 4-7 zone. You should be able to speak a few words but if you can sing a song without missing a word, increase the intensity. Sorry but when I see someone leisurely riding a stationery bike while reading a book, they are NOT working hard enough to burn fat. That would be appropriate for cooling down though.
I do recommend people have a small snack before weight training if they haven't eaten for a while and, if the session has been intense, feeding yourself within 30 minutes following the session to replace lost glycogen in the muscles. Preferably a protein and carbohydrate such as a smoothie made with whey protein powder and fruit. Adding muscle will add years to your life and keep your metabolism high, so if you're a female, don't worry about bulking up. Muscle is a girl's best friend!
Hope this helps!