I'm so confused, I'm just a beginner at all of this.
I have created my godaddy site already and published it. I have used the SEO tool to help it along some but I'm not sure whether I need to buy the hosting separately. When I do a google search for my page or even in the address bar I get an error message asking if I spelled it correctly, etc.
You can't create and publish a site without hosting. Thus, you already have hosting.
Google indexes content on it's own schedule. It typically doesn't happen immediately when you publish a new page. Wait a day or two and check Google again.
Likewise, if you just purchased your domain name today, the records that match it to your site's IP address may not have been updated yet. That could explain why browsers don't find it when you enter the address in the address bar. If you know the IP address for your site, try entering that in the address bar of a browser and see if your site appears.