What may be the easiest is to develop the site at Godaddy in a password protected directory. Without a username and pasword combination no one can even view you site. This is a standard cPanel management option.
Going live entails removing the password.
Developing on the site would entail providing the directory login at the start of your session, you would then login to WordPress as usual.
Advantages:
-you are developing in the deployment environment
-you can easily test the site from different OS, browsers, mobile etc.
-you get to learn how Godaddy really works, support etc, you will be able to learn this in your development time, rather than under the stress of live maintenance.
Disadvantages:
-you are developing remotely, doing lots of file edits and upload on each step.
OR you could proceed as you anticipated, install a webserver on your computer, develop locally, then export and upload to Godaddy after you have demonstrated the site on your computer. You are on Mac, so the software you need is called MAMP (Mac, Apache, mySQL, PHP), best to get the bundle rather than install and configure each separately.
Advantages:
-editing files locally, faster edit/test cycle
Disadvantages:
-not so easy to test the site from different OS, browsers, mobile etc.
-you have to become more of a sys admin, configuring and maintaining the server etc.
-deployment environment will be different from what you develop under, bound to be differences.
I think you should do both, have a local server for highly interactive work, like tuning css and developing javascript or php, and develop the content on Godaddy.
Whatever you do work with a child theme.
Also install filezilla as by far the best FTP program around.
If you install MAMP, then also install phpmyadmin
