>>the root of the repository must be the root of the website and after a commit should be immediately available in the browser
I will include the mode of boring and bring some clarity. The repository is not just a set of files and folders. The subversion repository uses organized in a special way the file system. Usually files are stored in the database, or the files of a certain format, so the root of the repository cannot be the root of the website.
With regard to the use of project files for its intended purpose, it is necessary, first, to export a working copy(svn checkout). It is a common tree of folders and files with a hidden subdirectory .svn in each directory of the tree. Such a local copy is available to each project participant, who commits to the Central repository. But this copy cannot be used in production, because it contains these same service subdirectory .svn. In order to get rid of them, exported a clean working copy of the svn export. Now this is your project.
Now is the time to develop a web project using svn, I can share how I have everything arranged.
VDS is on, where spinning the svn server. There are two branches of the repository trunk and release. On the local computer working copy as you develop comico all in the trunk. All scripts are tested for localhost. Development database the total, are located on the same server and svn.