It definitely is possible, and you should really read the WordPress Codex before diving in, and read it in-depth. It's very well documented and usually a simple Google search will bring up answers for many of your questions.
The WordPress Codex will explain everything for you, especially this page for your situation, regarding creating a theme. Pay attention to the template hierarchy as well to be able to customize certain pages without much work.
The Codex also has a Where to Start page that can be of tremendous use.
You can also check out other questions tagged with
<theme-development> for many common questions that WP developers have.
All I can suggest is read, read, read!
Edit: This page is also a good read to begin. :)
Hope this helps!