I can't give an official answer, but I'm 99% sure that the answer is 18. If you are younger than 18 and have a credit record, you might be able to get service in your name, but I would not count on it.
Family plans tend to be cheaper than individual plans (on a per-line basis) anyhow. If you want to save money, I'd try to go in on a family plan with friends and/or family members.
To add on , if you go the prepaid route there's no credit check and it shouldn't require
According to this paragraph on T-Mobile Terms and Conditions
When you accept, you're telling us that you are of legal age (which means you are either legally emancipated, or have reached the age of majority as defined in your jurisdiction) and that you are able to enter into a contract.
one must be of legal age to get any sort of plan under his or her name.
To my understanding, this Terms & Conditions apply to any relationship with T-Mobile and its customers along with seperate Terms & Conditions for each type of relationship.