I specify 1000px along the longest side. The dpi setting does nothing if you're specifying pixel lengths. The image ends up being 1000 pixels across. On a 2000px wide monitor it'll take up half the space. On a 600x400 monitor (if they still exist) it's fill the screen and overlap.
At 1000px, someone could do a screen grab and print out a reasonable 10" print or a really good 5" print. 1000px is about the best mid-way balance between size and quality on modern screens today. If you're really cautious about screen grabbing and printing etc, you can watermark (in LR) or go smaller. 800 is about as low as I'd go today though. Anything smaller and it starts to look like a thumbnail on modern monitors.
At 2000px you have an image that'll look really good on high rez monitors, but will be screen grabbable and printoutable to a decent 11" print and magazine quality 6" print.
tl;dr: Set the export to 1000px wide & high (LR will grab the longest edge) and ignore dpi. Golden.