It sounds like you’re reading a tutorial specific to a theme that has a Blog template, which isn’t standard WordPress practice.
If you want your home page to be your blog (latest posts), then the option you set in “Settings > Reading” is the way to do it.
Not sure what’s going on with your Podcast menu item – is it linking to the home page? Or a separate page? If it’s linking to a separate page, what’s telling that page to show posts?
If Podcasts is a category in the blog, you’ll want to add it to your menu using the “Categories” module on the left in “Appearance > Menus”.