For practicality's sake I'm going to tell you it's impossible to gain muscle while losing weight. If you are at a caloric deficit you are not going to have enough calories for muscle resynthesis.
First lose the weight, then concentrate on gaining weight back as primarily muscle. You cannot lose weight only as fat, you will lose some muscle as well. Same when you gain.
I'm not that much of a fitness expert, but here's my opinion.
You shouldn't hold off your weight training, muscle development is highly beneficial for your fat-loss. It keeps your metabolism high in spite of diet. If you'd go on strict diet with no exercise, you're more likely to lose muscle and store fat. I think the best option is to combine resistance training (for maintaining muscle) with some cardio (for fat-burning and cardiovascular health- which is important if you want to get big muscles) and of course a well-balanced diet with appropriate amount of protein and no more than 500 daily calorie deficit, as you'll need to fuel yourself for exercise and muscle growth. I think it's the most steady way to go. I'm not sure if you're into body-building - but if you do you'll need to educate yourself about proper pre- and post-workout nutrition as it is a crucial factor.
To conclude, I think it's okay to start with muscle training right away, with a small deficit in diet. As you slim down you just slowly go up with your calories till you get to your maintenance.
Depending on where you are starting from, fat loss is probably your main goal but you want to maintain your muscle while you do it so make sure you are including resistance training in your workout routine. This will help you lose inches and do the most for your body shape. Once you lose as much fat as you want, you can work on building some muscle with a caloric intake a little over maintainence if you want.
If you are weight training, you will gain some muscle. You are not going to put on lbs and lbs of muscles, but you will gain a little, enough to help with the calorie burn. Work on losing the weight, but do it by perhaps doing some dynamic workouts. I am currently doing workouts that include weights (low weight), but it's focus is endurance and calorie burn. It's not going to make me lose muscle, or be weaker, there is no way you can lift weight and not put on at least a little muscle... or make the muscles you have stronger (which means, putting on muscle).
You can do strength and weight lifting .. during your exercise, that will tone your shape and strength your muscles.
You will actually gain muscles during exercises .. I do Taebo since 1.5 month and I can tell you I see my leg muscles starting to appear and my leg is shaping like an athletic leg ... AMAZING!
I think you'll need to exercise to get toned. If you quickly lose a lot of weight without exercising and building muscles instead of the fat you burn, your skin can get loose easily (or you can call it waving muscles on your underarm :D ). Also, physical activities can lower your appetite, too, increase metabolism and help produce endorphin to make you feel good. So I say you should combine a good diet with good training.
Start lifiting, and definatley start HIIT. You may not lose a ton of weight but you can expect to loose a few pounds and you will replace fat with muscle