The most appropriate verb from the list to complete the sentence "John ..... a doctor." is 'become'. This indicates a future aspiration or a change in profession.
To make it grammatically correct and fit the context of a future simple/be going to, we can use 'will become' or 'is going to become'.
John will become a doctor.
Or
John is going to become a doctor.
Ответ: will become / is going to become