Good strength training exercises include pull-ups, sit-ups, push-ups, sprints, shoulder dips, handstand push-ups, jumping jacks, toe-rise, prone scissor kicks, lunges, and leg lifts. Light weights can also be used.
As a gymnast you want your body to be strong, but lean so you should do a high number of repetitions with light weights. Light weights will give you the resistance you need to strengthen your muscles without making them bulky. Bulk will make you heavy and slow you down which is not good for gymnastics.
For gymnastics you really need an all around toned body. Having a strong center is important, so doing crunches would be good. You also need strong thighs for pushing off the ground, lunges would be good. Hold a plank position for 30 seconds and repeat. Pilated would also be good.
well mostly core exercises are the most important but some fine motor skills are important as well so the list includes but not limited to; leg lifts chin ups levers heel and toe risers handstand work wrist strength exercises dips and also of course cardio vascular activities as well