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.