The syncing of photos using the Finder and a USB connection is somewhat limited. The photos cannot be deleted directly on the iPhone.
The easiest way would be to create a small Photos Library on your Mac with just the photos you want on your iPhone, then use iCloud Photos to sync the photos between your Mac and the iPhone (Use iCloud Photos on iPhone - Apple Support). This way you can manage easily which photos will appear on your iPhone and sync any adjustments and metadata between your devices. You will be able to use the synced iCloud photos the same way as the photos you save to your iPhone from the camera. They will be less limited than photos synced via USB.
You can still keep a larger Photos Library with all your photos on your Mac, as you can have several Photos Libraries. Only one of them can be setup to sync with iCloud and appear on all your devices.