Could anyone point me in the right direction?

I'm seeking some inspiration and examples by which to model after.

What are some typical poems that would be considered grade school (elementary thru grade 12) that all should have been exposed to?

Reading lists are welcome and appreciated.

Robert Frost's poetry was very prevalent while I was going through high school English

Edgar Lee Masters

I don't know if you consider Tolkien to be a poet, but there was a lot in his very popular writing.
My personal favorite is Robert Service.
Then there is Robert Burns:

Here is a list of some of the best known American poets. They run the gambit in topics and complexity and can be applied to different ages and classes.

Frost
Longfellow
Dickinson
Poe
Elliot
Pound
Hughes

This may help you:

https://www.poets.org/poetsorg/materials-teachers

Non-American

Shakespeare -Sonnets
Yeats
Wordsworth
Tennysson
Milton

Edit to add the Book of Psalms from the Bible.

Shel Silverstein

For those of us oldsters, memorizing a poem was common elementary school practice. Robert Louis Stevenson was a popular choice for that.