John, the term “Cloud” is a bit of a misnomer. With Creative Cloud the relevant program (in your case Photoshop) is downloaded and installed on your own computer, and you do all the work on your own computer. The files you create are stored on your computer. The only “Cloud” aspect is that you are able (if you wish) to make use of storage space in the “Cloud”. It’s not a requirement to store on the “Cloud”
You do not even have to be connected to the internet all the time to be able to work in Photoshop. Adobe just need to be able to check (I think once a month) that you are up to date with payment.
Just remember that if you stop subscribing to Adobe, the program will no longer work, but all your files you have created remain yours. Before signing up just check that your computer has the right specifications to be able to run Photoshop.
I hope this helps your decision making.