Best practice is to always use Place. Don't worry about the way the image looks in InDesign - that's just a screen preview. You can enhance its look a bit by using View > Display Performance > High Quality Display. Even then, what you see on screen is still a preview, and will not look as good as what will actually print.
Keep in mind that when actually printing, the data from the original Illustrator file, (not the preview) will be used for output.
There are very few if any scenarios in which pasting is preferable to using the Place command. The appearance quality issue you're seeing is a result of the Display Performance setting in the View menu.
Thanks. I'll go back and make the changes and proceed forward!!!