I don't know if Tortoise ships with a version of the svnadmin tool or not. But you would need that to first create the initial repository. Tortoise also might have a menu option or dialog to put a nice GUI on front of this process of creating the starter repository. Nevertheless, I'd still recommend you install the command line client tools in addition to Tortoise. TortoiseSVN might come with a standalone version of svn.exe, but I've had problems with the return codes and extra console windows popping open. I've been using SlikSVN as the command line client (no, that's no relation to us) for a while on Windows, and it works well. You *do* have to remember to keep your command line client and the TortoiseSVN versions up-to-date with respect to each other, as sometimes Subversion introduces breaking changes in the format of the working copy admin directories.
To set up version control in SlickEdit, all you do is go to the Tools > Version Control > Setup menu command, then find Subversion under the list of command line clients, and then click the Setup button to the right of the list. SlickEdit will try to find an installation of svn.exe for you, but if it can't find one in your PATH, you'll have to set up that full path explicitly.
When you set up version control, and you don't have a project currently loaded, you are setting up your "default" version control settings. When you have a project open, you repeat the same steps to set version control for that project.
