The form -(으)ㄹ게요 is a simple way to express your intent or to make a promise. This form is used in conversations with friends or family though.
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 verb ending -(으)려고 하다 you use to express the intention or plan of the subject. However, he or she has yet to act upon said plan or intention.
The form -겠다 is a versatile form that you will often hear in Korean. It expresses one’s intentions, one’s intuitive suppositions and the near future.
The Korean expression -기로 했다 indicates a promise to do something you have made with someone or with yourself. It is typically used in the past tense.