What's the BEST way to see customers who have recently purchased a product?

Use the Sales Logs report!

This report will be under Sales > Reports > Product Sales Logs. Add the Product Name and Contact Name as headers if they are not shown.

Then, create a group based on the product you are interested in using "equal to" or "contains" and then supply the product name. It looks like this:

After you save the group you can then adjust the date range here:

We have a lot more about creating sales reports in our KB article at this link!