AceCo55 pretty much nailed it: the PPI metadata field in an image file has no effect in digital display, including the web. You can set it to 1 or 1000, and there won't be any difference at all.
If you have the latest version of Photoshop, you should know that "Save for Web" has been replaced by an Export option in the menu. I guess it uses newer compression algorithms. The legacy Save for Web option is still there, but Adobe recommends using the Export function instead. Of course, if you edit your photos in Lightroom or any other application, use that software's export/save option unless you're dissatisfied with the results.
When I convert a raw file to an image file and need to choose its dimensions, I think about the dimensions of the output media. Some dimensions you may want to know, all in pixels:
- Ultra HD (the consumer 4K standard): 3840 x 2160
- Full HD (most common resolution right now in computer and TV monitors): 1920 x 1080
- iMac Retina 5K display: 5120 x 2880
- MacBook Pro with Retina display: up to 2880 x 1800
- The latest smartphones: up to 2560 x 1440
Generally, you'd want your image to have at least as many pixels as the monitor. So pick the kind of device you're aiming for, and size the image accordingly. I usually go between 2000–3000 pixels on the long end for photos that may be shown full-screen, or 1000–1500 for photos that are displayed smaller (e.g. part of an article).