There is still sufficient time to prepare for Google Photo changes. Right now you are not charged for smaller compacted version of you photos at all (they are not included in your Google Drive/Google Photo Limit). I'm not conversant with all the restriction on movies but short movies are also free, (but please check google for full details), Furthermore it is my understanding that any photo uploaded before the 1st June that are now free and not included in the limit will remain free and not included. This is a big "Get Out of Jail Free Card" for all of us with lots of google photos.
Google use the unusual term "High Quality" for these compacted files. They are any JPEG file that is less than or equal 2040 pixels along the longest side. Whereas it uses the term "original" for large files (and I presume RAW versions of files). So the first task is to compact all your files on google (and/or download the big ones). Fortunately google provides tools to do this.
FREE UP SPACE
This is really simple. You can access the tools by first click on the gear icon, top left of the google photos screen on your web browser. and the scrolling down in setting to first click on High quality which means any new photos you load will be staved in compressed format, even if they are larger when you upload them. Next click on the Recover Storage button, it will start looking through your photos and compress any that need to be. It will warn you this can take an hour or so.
Only click on that big blue Buy storage if you really need to. Even after the compressed files are being counted it will take a long time before your collection reached 15GB.