Can I design my website online?
If you intend to design your own website the best place to start would be on your home computer. Designing a website from the basics onwards online is simply not a viable option. So start on your home computer and once you are done with the designing and developing you can put it online.
If you try to design the site online you will have continuously upload the files to the site that you are using for designing purposes each time you make a change. This will be very time consuming. So doing it on your home computer is a faster option.
If you are using a UNIX based web hosting you can always install Apache on your home computer.