How the file is prepped is the most important thing. Here's what I do...
Sharpen the image properly in Lightroom to begin with.
Then, in Lightroom, choose output size, select sRGB, and most importantly "Sharpen for Screen".
Next, in Photoshop choose Save for Web, jpeg "Hi" Optimized.
This is what I've been doing for years, and seems to produce the sharpest looking web files.
Michael