Correct file settings for printing

IMO you should edit you camera max images size.  Keep all your camera pixels . Develop the image so it look pleasing to your eyes and then save you image.  Keep the file as you Master image.    When you have a use for the image like  printing.  Edit the master and create new document for print.  Crop the image to the aspect ratio of the print you want to make sure of the image composition that will be printed.  Then use Image size make sure resample is NOT checked. then set one of the print side to the size you want to print.  Photoshop will set the other side correctly and set the Print DPI resolution to print the image that size.  Only if the DPI is very low will you need to resample and intepolate your image.   What is very low depends.  100Dpi may be to low for a print that will be hand held and viewed up close.  100DPI will not to too low if the Print size is like 3 feet by 2 feet that will be viewed form some distance.

The other side of the coin is the image is for use on the web.  In that case after you make the aspect ration crop for the image composition you want on the web.  When you use Image size you would want to make sure to check resample set the interpolation method to use then set the number on pixels you want the imasge's width or height to be.  Photoshop will set the number of pixels the other side will be.  DPI is meaningless on the web  image are displayed by display pixels.  What ever resolution a display has the image dpi setting is not use for anything its meaningless.

The document DPI is Print Pixel size.    You printer dpi  setting is not Print pixels size it is a quality setting.   Ink jet printers paint in you image larger pixel using mant smaller droplets of ink.  The higher quality setting are only available when high quality photo paper is used foe more ink is layed down which would saturate regular paper.

Not quite sure exactly what you are asking, but printing bigger requires more pixels in the image.

8 x 10 inches at 300 ppi requires 2400 (8x300) x 3000 (10x300) pixels.

20 x 30 inches at 300 ppi requires 6000 (20x300) x 9000 (30x300) pixels.

A 20 x 30 print will probably not need 300 ppi, so for printing at for instance at 180 ppi you will need 3600 x 5400 pixels.

You can't enlarge a 2400 x 3000 image to 6000 x 9000 (well, you can, but the result will be very low quality), but reducing the dimensions does not lead to any quality loss.

You should also be aware that 8 x 10 and 20 x 30 are two different aspect ratios - 4:5 and 2:3 - so if you want to make a 20 x 30 print, the image must have a 2:3 aspect ratio.

For more information on how digital images work, see What is a digital image?