File size and image size are 2 different things.
Right. I hope my answer was clear on that.
Pixel dimension define the image size.
The Quality setting controls the file size.
I think this is almost correct. The quality setting
affects the image size, but it doesn't
specify an image size, so to the extent it controls it, it's only indirectly and imprecisely.
But - there should be a preview function that tells you what a scale setting will reduce the files size to.
As I mentioned, I don't have DPP installed, since I use LR, but I googled images of DPP's save screen and I don't actually see that file size preview function. Some of the free products above might have that, though. Paint.net, for example, computes a file size as you change JPG quality settings, but it doesn't let you target a specific size, per se.
I didn't see the OP specifically refer to needing batch-mode conversion capabilities, but it might be worth noting that this sort of preview is somewhat less useful in that case because you'd have to adjust your settings between each photo in order to target a specific size in MB, which sort of detracts from the utility of a batch mode.