How to maintain a local mirror on my Mac?
First, download MAMP.

Then, use MAMP to run Drupal locally (great info here, on drupal.org). Another option is the Acquia Stack Installer, but that's only better if you plan on running Acquia Drupal (at least, in my experience). MAMP is pretty powerful (I even have it, or XAMPP on Windows) running a few Intranets here and there).

You can either grab the files using FTP, and put them in MAMP's htdocs folder (or configure MAMP better, so you can put the files into your ~/Sites/ folder, for instance, using virtual hosts), or you could use source control, like Git or SVN, to manage your drupal site codebase—then just do a git clone to your computer and you'll have the entire codebase.

Use PHPMyAdmin or some other tool to download the database for your website, and then, using MAMP's installation of PHPMyAdmin, import that database into a database on your local computer. You'll need to make sure the settings.php file for your site can authenticate to MySQL on your local computer.

You can either set up a user for your local MySQL installation with the same password and username as your live server, or you can customize settings.php so it uses a different database name and credentials on your local computer. See, for instance, Suggestions for settings.php - Local dev, Development server, Live server