Hi welcome and congrats on your first cel.
The type of file you linked is fine but A4 size will likely be too small. I measured one of my douga/sketch (douga are a tiny bit bigger than standard size cels) and its 240mm x 270 mm. A4 size is 210mm x 297 mm so it's too small. B4 is a better size or even A3 is good too since it is big enough to fit backgrounds too if you plan on getting more cels in the future (edit: I realized I mistyped some of the A4 and A3 stuff but it's fixed now. Hope that wasn't confusing).
In my opinion it's not needed. If you get one of those clear books it should be enough support already. If you want extra support, sure go for it but the one you linked will probably be too small.
Either vertically standing up or hanging is fine. I have linked two pics of some other collectors methods of hanging if you'd like to see an example: https://imgur.com/a/F9vbN1t
I agree that humidity control is likely to be your biggest problem. Some people put desiccant (example: box ver or pouch ver) near their cels to help control the humidity around the immediate area the cels are stored. I saw another collector purchased a dry cabinet meant for electronics (like cameras) for around $300 (example here)