Problems about Verb!

My question is when can we use "to + Verb" and when "Verb_ing" at the first position in the sentence?
For ex:
_ "Think everybody used to be wonder the same where is the word O.K. from?" ---> Notice "think"
_ “To do so would be unwise!”
“Doing so would be unwise!” ( Which is correct and why?)
_ "To be a good student, I must study hard."
Please explain for me and give more examples. It's my biggest concernt about when I writte a composion.
I know that in my text, there're alot of mistakes. Please show it for me as well!
Thank you very much and wish you happy!

'To be a good student, I must study hard'
-- in order to become a good student, I must study hard

'Being a good student, I must study hard'
-- because I am already a good student, I must study hard