When working on images for the screen, set the resolution at 72 dpi because that is like zeroing your resolution ruler. It is one pixel per point, it is universally understood to mean 1:1 pixel ratio (show each pixel of the artwork in one pixel of the display) and it is the lowest sensible number because it corresponds to the actual resolution of the first graphical computer. There are no computer screens (or printers) with less than 72 dpi and never were.
One thing to consider when making this kind of low-res style artwork is to work in vectors. It is counterintuitive but has many advantages. You set up a grid in a vector drawing tool to represent virtual pixels, and you draw each pixel as a vector block that fills one square of grid. Then you can easily render your artwork at any size, for any purpose (Web renders at 1x, 2x, 3x, or a marketing poster image for example) and you can color with Styles, make a brush that draws the right sized block, and even color each virtual pixel with a gradient if you like. You can achieve the low-res style without actually suffering the disadvantages of low-res. That is a common technique for this kind of artwork.