DPI doesn't really have any useful relevance. For display on a monitor you just need to know how many pixels you need to fill? the screen.
e.g. my 17" laptop has a 1920x1200 display and my 40" TV has a 1920x1080 display. The DPI for the two displays is completely different (132 for my laptop and 55 for my TV) and completely irrelevant. I only care about the pixel dimensions I need my image to be in order to fit without further resizing up or down. So, when I prepare my final images I crop/resize to fit within a 1920x1080 maximum size. That way I know they will fill both screens as much as possible while never needing to be resized again to fit either display.
Hayley, if, for example, your laptop screen is only 1368x768 and you resize your images for a perfect fit then if you try to display them full screen on a display with a higher resolution (and potentially larger physical dimensions) then you will run into problems. Not only will you have insufficient pixels, but the very action of magnifying the images on the larger display is likely to make flaws more obvious to the eye, whether they be noise, focus, DOF, blur, shake or any other undesirable thing.
The best approach is to size your images to fit the intended display device precisely, or to only view at "actual size" and not to expand them to fill a screen with more pixels. Failing that, don't resize them at all, but keep them at maximum resolution and just let them be downsized (never upsized) to fit whichever display you happen to be using.