A couple of things. The permalink issue you are seeing might be caused by you trashing the /home page but not Permanently Deleting it. Check under the Pages menu to make sure you have destroyed all evidence of the page.
While you are there, create a page, call it “home” if you like, or “Welcome to my Awesome Website”, and don’t worry about the permalink.
Now go to Settings, Reading, and you’ll find options for setting up which page you want to establish as your home page. Choose the “Welcome to my Awesome Website” page as the Static page you want as your front page. This will make that page the one that appears when users go to your main domain. This would be an actual homepage (no subdirectory), rather than something that lived at domain.com/home.
You can then optionally go in a customize the menu that appears in your theme (depending on the theme: the BP default theme supports menus) In the Appearance menu, go to Menus, then create a menu using the options on that page, that will allow you to customize what people see on the top of the page. If you go to testbp.org, you’ll see a good example of a customized menu with “child” pages that dropdown from the main titles. Note that in that case the “Home” page is the blog, with the newest update rising to the top.
