When you have an image of 1600x1200pixels and you reduce it to 400x300pixels, Photoshop discards three out of four pixels.
To be honest: I didn't actually see it do this, but I read it in one of the "classic" books (bible, Gary Bouton, can't exactly remember which one. I'll look it up if you want to).
When you force PS to calculate and you choose bicubic, it takes into account every pixel that surround each pixel and calculates a mean value for this. This gives a better result.
But if you downsample in one big leap, then PS still has to discard too many pixels in one time. Which is why it is better to do it in several smaller steps. And to take care that none of the steps makes it easy for PS by taking, say, 50%. Better is to use values that are near 3/4, 1/2 and 1/4 (in your case, as you want to go from 1600 to 400) but not exactly 75%, 50%, 25%.
Hence the values I gave. These are "random" but I quickly calculated that they cannot be calculated easy.
Most probably, afterwards the image will be a bit blurry. Yet, if you sharpen it the usual way (unsharp mask,...) the stairsteps of the jpg might become more visible.
Sharpening has in fact little or nothing to do with sharpening. What is done is in fact nothing else than accentuating the edges by adding contrast to what is lighter and what is darker.
Therefore, an edge-mask is best to get good sharpening.
The procedure and settings come from Deke McLelland. But, seen the fact you can find them on every photoshop site on the net, I don't think I do something illegal by giving the method here.
1/ Open the Channels pallette and duplicate the channel with the best contrast.
2/ With only this active, Filter>FindEdges
3/ Image>Adjust>Invert (Ctrl/Cmd+I). You now have whitish lines on a dark background.
4/ Filter>Noise>Median This averages the pixels. Radius of about 2 is perfect.
5/ Filter>Other>Maximum This makes the whites broader. Radius here appr. 4
6/ Filter>Blur>Gaussian Blur. Same value as Maximum filter
This is your edge mask
7/ Now return now to composite view, but stay in the Channels Pallette
8/ Ctrl/Cmd-click the name of the mask channel you just created. This loads the mask as a soft selection.
9/ When you use Unsharp Mask now, it'll only enhance the contrast in pixels that the mask allows, and these are the edges or, in other words, the transitions of tonal values that were different enough to be accepted in the settings we chose. You can now set Unsharp Mask to maximum aount, and some 2 pixels Radius.
Forget about threshold.
I won't be able to answer more today, but in some 24h I can be back if you have questions.
Hope this helps. I know it's not the easiest way out, but that's the way we really learn.
But, realy: if you intend to post photographs on the web and you can, it's best to take that extra pic at the size you will upload. A few kB, and the best quality you can get.