Use the barbell step-up to develop balance, coordination, core strength, and unilateral lower body strength.
The lunge is a brilliant exercise, helping you to develop coordination, balance, and the unilateral (one-sided) functional strength of your lower body.
Use the cable down-up twist, an isolation exercise, to strengthen and stabilize your core, and to strengthen the twisting movement pattern of your torso.
Use the barbell front box squat to strengthen your front squat strength. It's also useful if you have knee problems, as it requires less weight.
The bodyweight squat is great for learning the very basics of squat form, such as how to keep your head up and torso upright as you descend.
The cable horizontal Pallof press is a very effective functional exercise to use to strengthen your core's ability to resist rotational or twisting forces.
The side plank hip adduction is a decent exercise that you can use at home to strengthen your core and work your inner thighs.
The lying single straight-leg hip extension is not an effective exercise for overloading your hamstrings. Use it only when you do not have access to a gym.
Tone your inner thighs with the cable hip adduction, an isolation and pull exercise that targets your hip adductors (adductor magnus, longus, and brevis).
The Smith machine bent-knee good morning, an isolation exercise, targets your gluteus maximus. Movement in the knees should be kept to a minimum.