I am looking to get braces through Cigna insurance. I have a major crowding issue and believe I need some pulled (Photo)

This is only my top row although my bottom is not much better. I am 18 years old and definitely want more confidence through my braces however I do not want something so noticeable for years. What do you think the best option would be? Am I able to have different types of braces thoughout my journey? Also, I am turning 19 this year so do you think my insurance will stop after I turn 19? Lastly, do you think I could have straighter teeth by 21?

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