We use all of them in our daily conversation.
行こう and 行きましょう mean the same, "let's go".
(行こう is the informal/casual form and 行きましょう is the formal one.)
行くだろう and 行くでしょう mean the same, "will go"/"I think (someone will/may go", about "to go" in the future or guess/supposition".
(行くだろう is the informal/casual form and 行くでしょう is the formal one.)
I hope this was helpful.