Recommendations for web app deployment / source control

I'm involved in ongoing development of a Linux (Ubuntu) web application and using Git / bitbucket for source control. Until now deploying the web app has been manual. We would check out the code and then move the files to the appropriate directories.

We want to automate the deployment. One option is to use a source control directory structure that mirrors the deployment directory structure and check out the code directly. For example, our web pages could be in a /var/www/html directory, while our cgi bin scripts would be in the /usr/lib/cgi-bin directory. In that scenario, I assume we would cd / and checkout the code. We don't currently have that structure, and I don't want to change it unless it will be beneficial. Another option is to add a file that specifies where files are supposed to go (at the directory level) and have a script copy the files.

I'm sure there are better alternatives. Any advice is appreciated.

Thanks.