This all depends on the resolution that you upload to the internet. If you intend to upload your images at full resolution (meaning that you do not re-size the original image to a lower resolution), then you will be fine only using the sharpening tools in the development module. However, if you intend to re-size your original image to a lower resolution, then you will want to use the "sharpen for screen" option during export.
If you run a good sharpening routine during RAW development, then you will most likely use the "low" setting for output sharpening amount. If you are resizing your images for upload, the amount of output sharpening will also vary slightly depending on how much you reduce the original image resolution. Today I re-size all of my landscape oriented images to 1,100 pixels on the long side, and I re-size my portrait oriented images to 860 pixels on the long side. In both cases I use the 'low' setting for output sharpening. If you are re-sizing your images for upload, I recommend you test a couple exports using the low and standard settings to see which fits your style best.