You can certainly, if you wish, use your Blogger blog and develop that as your home. Consider also, though, whether you might want to try WordPress (free or paid), Typepad, or another hosting service. Some of these come with domain name service, so if you'd like to have your name or your blog's name "in the clear," they might be worth considering.
Once you've settled these issues, there are two more to consider: design and connection. Do you want to refine a design you already have, using the basic tools available via these services? Do you want to design your own page from scratch using software such as Dreamweaver? Try a free web design service, or hire someone? And then as to connections: where do you want your blog or home to be listed? Do you want to link it up with your Twitter or Facebook presence? And what kinds of links to other people, resources, and services do you want to have? Do you want to have advertising? Do you want to put up a big neon sign? Or would you rather have a much "quieter" online existence.
If you have your own content -- fiction, poetry, film reviews, photographs, short videos -- do you want to use your site to help market it? If so, how would that affect your design choices? Or would you, as some creative people do, prefer to have one "public" presence and one more "private" one shared only with friends?
The final project asks you to identify your goals, modify and/or create your site, and then write a reflective essay of 1500 words on the experience, the decisions you made and the reasons for them, and your hopes and expectations for the future.