Let's look at some of the things you can experiment with within the squat. I will cover the bench and deadlift at a layer date. There are a few undisputed aspects to squatting that should never change. You have to keep a neutral spine in your lower back. You have to keep your upper back tight. You have to keep your chest up and you must not let your knees bow in. Beyond that the squat is really open to your own interpretation and there are a great deal of things you can experiment with.
First we have hand position. You can vary the width of your grip on the bar. A very narrow grip makes it easier to maintain a tight upper back and can be great for new lifters to help reinforce this. On the other hand it requires much greater flexibility in the shoulders and can lead to shoulder and bicep problems down the line. If you have very wide shoulders a very wide grip may work for you almost touching the plates. Any grip inbetween may work best as long as you are able to do it pain free and still maintain a tight upper back.
Next are the thumbs. Do you wrap them around the bar or not? Some powerlifting federations do not allow a thumbless grip so bear that in mind if you compete.
Then comes the wrists. Conventional form tells you to keep you wrist straight to avoid weight bearing on them. Personally I find this massively increased the stress on the shoulders so a bent wrist is also fine as long as the upper back is keep tight and the weight maintained on it.
Next we have bar position. You can go low bar or high bar. Traditionally low bar is seen as giving you better leverage but this may not always be the case. Some people are stronger high bar and many great powerlifters have used the high bar technique. High bar also makes it easier to hit depth and targets the quads better than low bar.
When I first learnt to squat I read starting strength and followed the advise on form. Low bar squat narrow thumbbless grip straight wrists. I found this position very uncomfortable especially during the bottom of the squat. I found the tension on my shoulders would cause me to cave in at the bottom lose my upper back tightness and in turn my lower back position. After some experiment and talking to a powerlifting coach I changed my technique to low bar slightly wider grip with thumbs wrapped round the bar and slightly bent wrists. All the tension on my shoulders was gone and I never had any problems in the bottom of the squat anymore. My point is not that Starting Strength is wrong just that that technique didn't work for me. My way of squatting fits my own body better.
After bar position comes head position. Some prefer to look up while squatting, others may find they tend to over arch their lower back if they do this. Others look straight ahead and others keep there head in line with their spine so will look straight in front of them at the top and a few feet in front of them in the bottom however you may find that your back rounds and have a tendency to fall forward. Do that which feels the strongest and most comfortable.
Next on the list is your stance. Many strong squatters especially geared ones squat very wide. Squatting like this emphasizes the hips and back more. Generally the narrower your stance the more emphasis is on the quads and the more upright your torso would be. A wider stance may not be the strongest for you though. Personally I find a wide stance gives me no power out of the hole unlike my shoulder width stance. Some lifters find a wide stance beats their hips up and makes it harder to hit depth aswell. A very narrow stance would hit your quads more but you could be lacking in strength due to not fully utilising the larger posterior chain muscles. Experiment with different stances wide and narrow to find which is strongest for you. There is also the angle of your feet which in turn affects the angle of your knees. A wider stance generally requires a greater foot angle.
Now it's time for the descent. Some may use a very exaggerated sit back really pushing the hips back while others may appear more upright. A good sit back allows a strong hip drive on the way up but too much may turn your squat into a good morning. If you are a more quad dominant squatter you may find less of a sit back stronger for you. Then we have the rate of descent. Some will descend very slowly and controlled while others may drop quick and attempt to bounce out of the bottom. A slower descent would allow you to pin point the exact depth you need to go without going to deep. A drop and bounce squat can make you stronger out the bottom but you will be going to greater depth. Also there may be a greater risk of injury from the drop technique. You could use either of these approachs or you could be somewhere in the middle. I used to drop fast and bounce but in an attempt to stop myself going ass to grass everytime I have adopted a slower more controlled descent.
When coming up for a squat you must of course push with your legs and drive with your hips. But there is also the elbows to consider. some people prefer to drive their elbows up. Others find this causes then to topple forward. Some prefer to drive their elbows down which can reinforce the lowerback arch and help them stay upright.
When it comes to breathing you should take a large breathe tense your abs and hold it. Then squat. You may prefer to keep your breath held through the duration of the lift. Some prefer exhaling while keeping the abs tense upon rising. This is also known as power breathing. Others still wait until they hit their sticking point then exhale forcibly. Again experiment and see which is strongest.
Of course no discussion about squats could be complete without talking about shoes. There are two real choices here. You can wear Olympic lifting shoes with a heel or flat shoes such as converse or wrestling shoes. Olympic shoes will make it easier to hit depth, put slightly more emphasis on the quads and keep you upright. They also give you a very solid base to push from. Oly shoes can only really work with a narrow to medium stance. A wide stance would require some weird ankle flexibility and make it hard to push from the heels. Flat shoes tend to emphasize the posterior chain more and require greater flexibility to hit depth. Those who squat wide all tend to wear flat shoes. Converse are a favourite of powerlifters although I'm not sure why. I find them too squishy to squat well in. Some other options are wrestling/boxing shoes or old school plimsoles. You don't get the solid base of Olympic shoes with flat options like converse or wrestling shoes but you can get specialist flat squat shoes made for powerlifting but they will set you back a fair bit of money. I would suggest when first starting out to go for cheap flat shoes. You if you decide a wide stance works best then you may want to stick them and invest in some specialist ones further down the line. When experimenting with medium or narrow stance squats you can try squatting with your heels on a 1.25kg plate to see if a heeled shoe may benefit you. If this is the case then a pair of Olympic shoes may be a good investment.
That pretty much covers squatting. As you can see there are a lot of small changes and tweaks you can make. Take your time and slowly experiment with them until you find your final form. Do not make radical changes but small adjustments to technique using trial and error. You need to squat in a way which works best with your own leverages, biomechanics, muscle dominances and goals. Squatting for big quads might require a different technique to squatting maximal weight. Or not, who knows? Squat the best way for you not just how your favourite powerlifting or bodybuilding icon does.