Resolution is physical size. That's the determinant.
The image itself is only pixels. This is important! Get to grips with this concept right away. Just pixels. It has no dimensions, it has no resolution. It's just an array of pixels, so many wide by so many high. This is the image size as Photoshop works with it.
Now, to print this, you need to decide how big these pixels should be on paper, the pixel density. That's where resolution comes in, and the physical print size is determined by how many pixels per inch. This defines a physical size of the pixel array.
The whole thing is given by the pixels per inch number. Just stop and consider what pixels per inch means. Read it literally, it means exactly what it says. No hidden meaning.
Now, you can use that inversely. If you have a ppi requirement, a certain density required, and you also have a requested physical print size, you can determine how many pixels you need in the file.
All these are straight calculations. Luckily, you don't need to take out your calculator, you can just let Photoshop's Image Size dialog do the math for you.
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What resolution / density is required for print varies. In high quality book and magazine print the standard requirement is 300. Newsprint will usually require a lot less, perhaps 100-150. Large posters/banners/billboards can go as low as 10 or 15 because they will be bigger, but seen from much farther away.
So find out what ppi is required in this case, and at what physical size. With those two numbers, you can calculate how many pixels the file needs to have.
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