Resistance training and cardio will both aid your fat loss goals tremendously. Exercise will consume calories, improve insulin sensitivity, promote a leaner body composition, improve cellular metabolism, and raise your resting metabolic rate. Despite this fact, diet is still going to play a major role in your fat loss goals. Check out
Jodi's guide to help you get started on the path to a leaner physique.
It is my opinion that resistance training should take precedence. Don't make the mistake of thinking you will turn into a massive bodybuilder over night. This is not an issue, particularly for a female. It takes years of dietining, training, and drugs to achieve the physiques that professional bodybuilders have. The lean mass that you put on will only enhance the shape of your physique and increase your basal metabolic rate. There are also numerous health benefits that go along with resistance training such as strengthening your joints, improving bone density, improved flexibility, etc.
I woud suggest beginning by training 2-3 days per week. Something like Monday, Wednesday, and Friday or Monday and Friday would be a good schedule. Just try to stick a day of rest in between sessions. Begin with compound movements; if your body weight offers enough resistance then start there. For now, skip the curls and kickbacks. Check out
my guide to designing a full body resistance training routine. If all you do is go perform a few sets some bodyweight squats, pushups (On your knees if need be), assissted pullups, and maybe some situps, then you will be on your way; of course, I'm assuming these exercises provide enough resistance to be optimally beneficial.
In terms of cardio, I do not recommend doing cardio in a fasted state. Although this method is highly effective, it is certainly a risky endeavor. You increase the chances of having your skeletal muscle broken down to aid the proper function of various energy pathways. You want to maintain or increase your lean body mass while decreasing body fat to achieve the physique you desire. If you eventually have to resort to doing this to achieve your desired body fat level, then at least ingest some protein or branch chain amino acids before the jog to help prevent muscle breakdown.
Start by performing some solid state cardio for 30 minutes or so 2-3 times per week. If you can only handle power walking for 30 minutes, then start there. That's fine. If you can handle some light jogging, then go for it. Just make sure to progress little by little, either by increasing duration or intensity (Jogging faster). Once you get into the swing of things and improve conditioning a bit, then you can start searching for more advanced forms of high intensity cardio to supplement you solid state: HIIT, Guerilla, Max-OT, etc.
Good luck. Stick with it for life. Don't let exercise be a path to weight loss and then give up on it!