The best exercises, contrary to most fitness advice, should deemphasize specific muscles.
Isolation exercises, which are mainly single-joint movements but include anything that focuses on a muscle, place too much shearing force on the bones and joints. They also train the muscles poorly.
The length-tension relationship shows that muscles create more tension, the main signal for growth, at medium lengths. Near the endpoints for the range of motion, the parts that bind within a muscle to form this tension spread too far apart or overcrowd. The joints have to work in weak positions here too.
Isolation then makes an exercise worse. You may feel like you are being productive due to the range of motion, yet you reduce the main stimulus to build size and strength.
We should use exercises in which no muscle dominates. Use medium grips, stances, and positions. Avoid too much range of motion. Avoid all extremes. Uses lots of muscle together. You can then focus on getting stronger, allowing everything involved to grow safely.
Most experts recommend the opposite. They ruin good exercises like the bench press by suggesting a close grip. They taint the great compound exercises through isolation.
The low-bar back squat, done with a barbell, is all you need for the lower body. This version has you place the bar across the top of the rear deltoids and middle trapezii. It achieves the right balance point, evenly working the muscles of the hips, knees, and ankles. It brings in the core, especially the lower back. The inner thigh and outer hip muscles work to stabilize. Small muscles in the legs and feet keep you fixed to the ground.
Avoid everything else for these reasons.
Tools
Avoid using a foam pad around the bar. This has nothing to do with acting tough; it would be sensible to use a cushion for the upper back if it had no drawbacks. It would even be fine if you just wanted to feel more comfortable so as to work harder with less to think about.
The macho attitude that defies this logic is like that for excessive range of motion. On the squat, many trainees will go far below parallel for its own sake. This will round the spine and harm the hip flexors. It serves no good purpose but to inflate the ego.
You should avoid using the pad because it forces you to use the high-bar squat position. This overstresses the quads, destroying the knees. It places too much weight upon a narrow area of your upper back. It makes you more likely to tip forward due to the greater distance between the barbell and the active joints.
Avoid using the manta ray attachment. It may aim to reduce stress on the shoulders but carries similar risks to the pad. It adds another thing to account for as you squat. The bar may wobble at the top. Without the barbell touching your body, you could lose the mind-body connection that helps with your attention on the exercise.
Avoid the safety squat bar. This shifts the weight to a high-bar position as well. Trainees also mention that they have to concentrate on not falling forward.
Avoid the buffalo bar. Since the hands have to rest a tad lower to hold it, this may keep the shoulder blades less tight. The camber of the bar, however slight, can reduce your control, while making it difficult to remove from the power rack.
Dumbbell squats will limit the weight you can use. It demands too much grip strength, a flaw that affects thick bar training. It has the disadvantages of the dead-lift.
You must avoid all machines, to squat or otherwise. A Smith machine restricts you to a path that is unnatural. Machines like the hack squat have too much movement at the knees without engaging the hips. All machines fail to activate the core well.
Variations
A barbell front squat brings even worse issues than the high-bar squat. Your hamstrings, meant to co-contract with the quads to protect your knees, shorten too much to contribute.
The zercher squat places the barbell at the pit of the barbell. Besides reducing the weight possible, it brings the same disadvantages as the front squat. It can also feel difficult to breathe.
All unilateral exercises reduce stability, shifting your center of gravity with a poor base of support. This has the prime movers work less intensely, and the spine gets loaded unevenly. For the Bulgarian split squat, the rear leg gets placed awkwardly behind you just like with lunges.
Use the Low-Bar Back Squat with a Barbell Only
By seeking and blundering we learn.
– Johann Wolfgang von Goethe
Many will suggest rotating through a bunch of these exercises for the sake of variety. They may say to pick an exercise among them to train your weaknesses. Sometimes they tell you to do this to work the muscles that struggle somewhere throughout the range of motion for a major lift.
This is all a mistake. You cannot treat weaknesses through dysfunction. Use the right exercises in good form and with less weight if you have an injury or some other issue. The fault will improve in time.
The barbell is the best tool for the squat, if an imperfect one. Ideally, the hands would be in front of the body.
Unfortunately, all of the variations move the weight too far away from the balance point. Choices like the trap bar deadlift fail us since they overuse the hip extensors and encourage rounding of the spine.
If your shoulders hurt on the squat, try going a bit wider with your grip. Avoid the bad habit of pushing up or pulling down on the bar. Keep a firm grip, but do not squeeze too tightly.
Use the low-bar back squat with a barbell only. This will train all of the lower body muscles well and safely, so ignore everything else.