There are some issues about monitor resolution, image size and quality, file size, print size, and pixel count (pixels per inch or ppi) to be considered here. There are several variables involved in this matter which make it complex. So, as an approach to understanding, let's look at just a few of the fundamental factors involved, and avoid using the term "resolution" for anything except monitor image size in terms of pixels.
There is a distinction between factors that affect graphic material to be viewed on a light producing monitor, and that which goes to a printer to be viewed on paper seen by reflected light. In either case, digital data or pixels are the source of an image. They are literally the building blocks of the image. The concentration of pixels (ppi) within a given area determines the level of image detail that is possible both on screen and in print. Up to a certain point (Epson says that point is 360 in prints), the higher the ppi the more detail is possible. The way this ppi is decided is quite different on monitor screens from that on printed material.
First, the printer side of the story. Each image file contains an instruction to be interpreted by the application that opens the image file, and subsequently by printers, that details items such as image size and the number of pixels per inch or dots per inch to be used in applying ink to the paper. To understand the relationship between ppi and printed image size, consider that within a given file size, there is a profile of related values of ppi and image size that vary inversely. If the ppi figure increases, the print size decreases. If ppi decreases, size increases. The total number of pixels in the file remains constant. When there is a change made in the file instruction which causes movement of these two factors outside the profile relationship, then the file size (total number of pixels) changes. That is the case when you decide, for example, to keep the ppi the same and change the print size. In prints, these quality choices of image detail and image size are arbitrary.
Second, consider how the image file is interpreted on a monitor screen. A computer's graphics card knows the nature of possibilities and limitations of the monitor to which it feeds data. The card itself carries inherent limitations. Generally, 128 MB of video RAM is sufficient to produce high quality images. What determines pixel concentration or ppi on screen is set by hardware, unlike the print which quantity is recorded in software. Screen resolution is chosen from a profile of possibilities offered by the graphics card via the operating system. If, for example, a resolution of 1600 x 1200 is chosen for a 16" wide screen, the ppi for all data it shows is 1600 / 16 or 100 ppi. On the same screen 2048 x 1536 yields 128 ppi, and 1024 x 768 yields 64 ppi. Again, the more building blocks in each inch of display the more information is available to see. So, at any given resolution setting (number of pixels, horizontal first, then vertical), all image files are displayed with the same sharpness quality regardless the ppi setting or the output size contained in the image file instruction mentioned earlier. At the given resolution setting, the image size is determined by the number of pixels in the width and the number of pixels in the height. Another way to state this is that image size is determined by file size, other things being equal such as colorspace bitrate. The amount of detail possible has been decided by the existing screen resolution setting. Of the quality choices between detail and size, what is available on screen is the choice of size, not detail.
So, the route to splendid graphic detail on a computer screen, in my opinion, is a graphics card (not a motherboard that contains a dedicated graphics chipset) with a minimum of 128MB memory (vintage 2002 or newer), and a monitor that will provide pixel density (ppi) of 90 or greater.