Intervention/Image is the best PHP image manipulation library that I know of.
Docs on that here: http://image.intervention.io/getting_started/installation
It allows you to resize, alter, save ("save" means saving the image and altered versions of it in some directory), etc.
If these images are going to be public, then you can store them in the public directory. If not, I would store them in the storage directory.
When I save the images, I "save" or "store' them in a directory and I save the location of the files in the database.
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