The form -(으)ㄹ까요 is a form with multiple uses. You can use it express your supposition in the form of question, ask for an opinion or make a suggestion.
The form -(으)ㄹ래요 is a casual form to either ask for someone’s decision, opinion or intentions; or to express your intention, plan or decision.
The formal form -(으)ㅂ시다 let’s you make suggestions or proposals to do something to others. It is a form with a few restrictions on when it is proper to use.
-(으)시겠어요 is a formal and polite form to ask after someone’s preferences or to make give a suggestion. It has within itself the honorific marker -(으)시-.