Want to know if I can have 2 sites or should be 1

I have a charity site smilesphilippinescharity.com and I wanted to add a blog to it. When I added a page it comes up with the same theme and eveything as the main website. Would it be easyer, as a beginer to site up a new blog seperate and link it some how. If I was to do this would it go under smilesphilippinescharity.com/blog ? If it is seperate do you load wordpress in this new sites files. Also can I put wordpress on my home computer to learn and work on a new site and uplosd to host later?
Thanks
Rob