How can I keep image quality when resizing multiple photos in Photoshop?

Obviously, the fewer the pixels, the less detail the image can hold. But even aside from that, any resampling will soften a pixel image. The common practice, that we all do, is to carefully resharpen after resizing. 

The operative word is “carefully”. Don’t overdo it. I know it’s tempting. What I usually do is set a certain sharpening that looks appealing, then dial back 50%.

Use the ACR filter, where you can control artifacts and halos very well. Play with the sliders and see what they do.

Image Size has some sharpening built in, but personally I don’t particularly care for the result. The “Bicubic Sharper” algorithm looks horribly oversharpened to me. I’d recommend “Bicubic smoother”. That doesn’t actually make it smoother, it just means there’s no built-in sharpening, so that you can better control it yourself.

The proper amount of sharpening depends on a lot of things, not the least image content, so it’s not possible to give fixed numbers.

Always view at 100% to assess sharpening and noise reduction! That’s important. 100% has nothing to do with size; it means one image pixel is represented by exactly one physical screen pixel.