Crochet hook size depends on the weight/size of the yarn. They can go from very tiny to giant size, really. Maybe a nice set of multi-sized hooks in a zippered case? I've had one of those for decades.
I would think just about any cotton yarn would be good for the granny squares. Some acrylics are very soft/pliable, some not so much. Probably a sport or worsted weight would be good. They are a bit finer than some of the heavier/chunkier yarns. It's kind of like fabric...feel the hanks of yarn. If they feel yummy in your hands, they'll pretty much feel yummy in whatever you/they make with them. If you're doing online shopping, I'm absolutely no help as I've not shopped for yarn in forever so no clue as to brands/types on the market these days but I'm sure some others will be along shortly with that info.