How to transfer photos from one computer( not I cloud ready ) to another computer that has I cloud using a photo stick

My old Apple computer is not "I cloud" compatible.

I want to transfer all my family photos to my newer computer that is "I cloud" compatible. I understand I may need to buy more storage. That said, can I accomplish this by using a Photo stick? Downloading photos from the old Apple Computer and uploading from the Photo Stick onto my new computer that is "I cloud" ready.