Hide photos that have already been cataloged

Thank you everyone for your recommendations.  I will work with Keywords as suggested and see how that goes.

Whichever you chose. Collections or Keywords LR will place an icon badge on each image that you have eother placed in a collection or assigned a keyword to.

So that is one way to identify which images have been placed in either a collection or had a Keyword assigned.

As John says below, keywords are a far better way to categorize subjects in your images. That also allows you to easily find for example photos of birds AND flowers as it is easy to search for multiple keywords. Collections are more useful for things like "Pictures from my July 2014 vacation", "Joe and Mike wedding", "Best images from photoshoot 10-2-19", "all-time best images" etc. i.e. looser associated images. 

When  you select images for a collection do you flag or rate them? In addition to being able to filter on keyword as mentioned by John, if you  use a flag or a color label for example  you  can use  the sort feature to quickly exclude images that have been  placed in collections.

"I intend to organize them by collection (People, Places, Birds, Flowers, etc.)."

I strongly recommend that you use keywords rather than collections for this -- keywords are designed precisely for this kind of organizing. While you can use collections, you'll find many rough edges in the user interface, and you'll never be able to share your organization with others (whereas keywords can get written into industry-standard metadata fields of exported photos and are displayed by other apps and online services).

You might consider a tutorial such as one of Victoria Bamptom's books: https://www.lightroomqueen.com/shop/

To see photos that don't have keywords assigned to them, do Library > Enable Filters and then use the Library Filter bar:

You can find photos that aren't in any collection, using a smart collection defined with this obscure criterion: