Firstly all "toning" means is losing the body fat to expose the muscle undreneath. If you intend to squat to build a bit of muscle in your legs and bum and lose fat you wont be able to do this at the same time, or at the very least it is extremely difficult. So i would first decide whether you want to lose fat first then build or build then lose fat. Personally though my advice would be, providing you aren't fat, build ass muscle first by doing target anabolic exercises such as squatting. If you do it properly and start to see gains on your ass, you may find that after a while there is more muscle for the skin and layers of fat to hold on to giving you a nice curvy bum shape, meaning you might not need to lose as much fat as you think, depending how much fat you put on during the anabolic stage (which can be controlled trhough your diet).
Having said that whether you choose to a catabolic or anabolic regime first, you should introduce squatting into both regimes as you will benefit from doing it no matter what. In an anabolic regime you will benefit from added strength and mass, in a catabolic state you will benefit from not losing as much if any muscle mass. You may start to see strength gains and you'll burn more calories when resistance training due to a metabolic increase in the recovery stage after exercise.
Lastly you will only get so far with body weight exercise. If your legs are relatively weak then you will see some strength gain, I doubt you will notice any mass gains unless you have very little muscle in the first place. Eventually you'll get to a stage where the body weight exercise you are preforming is merely an endurance exercise rather than a hypertrophy/strength exercise. Thus I would suggest doing weighted barbell squats and increasing the resitance gradually to ensure you are always gaining. However don't expect to go from a flat bum to an athletic curved ass over night. It may take weeks to see any visual difference, and it may take many months to reach your ideal goal, depending on how hard you train, how good your diet is etc.