Printers always ask for 300dpi which for us is actually 300ppi (pixels per inch).
This gives a resolution that nobody even with 20/20 vision will be able to detect any pixelation.
Now you have to do the math, but you first need to know how large the image you are sending will be printed, or displayed on a screen at.
When it will only be displayed on a screen then you need to think about how much the end user will be zooming in to examin the image.
So, keeping the 300 ppi in mind do the math of how large of an image you have to send so that when the image is stretched on to a sheet of paper or when the image is zoomed in on a computer screen, the resulting image will still have at least 300ppi for a monitor or 300dpi for printed paper.
But, how can anyone calculate the ppi per image size, ie the density of pixels on a monitor if you don’t know what the resolution of your clients monitor is? (to further complicate things).
You could play it safe and just send over a ridiculously large image with an insanely high ppi to make sure that no matter how much an image is stretched it will still retain a minimum of 300dpi or ppi but that would be irresponsible because your files would be insanely large for no reason.
So, you have to do the math to send over the minimal file size for the production you want.
When you print a pdf with Chief and chose 300dpi then Chief will print a pdf with 300dpi given the size paper you selected and the math will be done for you as long as the image contains only vectors but if there are raster images then those image may be stretched to a point where you lose the 300ppi threshold.
So, we’re back to math again. There’s no way of escaping it.
Nobody, absolutely nobody ever does the math. Although you can look up videos on YouTube and learn but I don’t suggest you do that.
The best way is to print to pdf at whatever size paper you think is appropriate. I use tabloid size.
Then open the pdf and zoom to the “actual size” (command 0 on a Mac) so that the image on your screen is to scale.
If you are happy with the quality but the file is still a little large then maybe try reducing the pixel density and do the experiment again until the file size is manageable and the image quality is to your liking. This procedure works because the resolution on today's monitors are quite high, so if it looks good on screen at scale then it will definitely print well.