Literally speaking, the speaker asks for a number of things in this poem. He asks for a tall ship and a star to steer by. He asks for a merry yarn and a good sleep after his long trick. He asks for many other things in between. So the real issue is to think about what this means in a figurative sense.
Figuratively, I would argue that the speaker is asking for freedom and excitement. Although he feels compelled to go to sea, his words about the sea are full of the language of freedom. He wants to hear the sails cracking and the wind driving him along. He wants to be like the gulls and the whales. These requests convey to me an image of freedom and of doing things that are thrilling. He is not chained to a desk in a closed room or to any other sort of mundane thing on the land. Instead, he is out there on the ocean, pitting himself against the elements.
Figuratively, then, the speaker is asking for a fulfilling life. One in which he is free to do what he wants and to challenge himself. Afterwards, he wants a good rest, but while he is alive, he wants to live life to its fullest.