Funny - my "target file size" isn't greyed out, but when I set it at 1000KB the results ranged from 440KB to 970KB - maximum size perhaps? I do have Quicktime as it happens (btw, I couldn't find the info about Quicktime and there seems to be no helpfile).-suleika
I also tried setting it at 1MB and had sizes ranging from 400-800kB. So I ran one pic through at size constraint of 1024kB which resulted in a file ~630kB and then I ran the same pic through saving at 100% quality which resulted in a 1.40MB file, (both times set at a resize of 'short side=1000').
I then compared the two using BeyondCompare's picture comparison and found there was actually minimal differences between them.
I tried the above on different photo subjects and every time it resulted in only minimal differences between the two output files.
You don't get told about Quicktime unless you don't have it installed, (which I normally don't), then it opens an info window. Doesn't say it needs it for the 'final size' output option though.
The help file is a PDF download from the author's WWW site
PictureScaler User Guide.
I had another better google session and found some other resources - I've just tried JpegResizer - created a batch between 820KB and 1040 - that's pretty good. I shall probably go for it.
Link five in the Google search in my original post

I'm sure there's probably a freeware alternative to these programs - just requires a little digging.
EDIT: Sourceforge is your second friend
kf-jpeg-fitsize - Fit jpeg to a maximum filesize. Reduce jpeg quality to fit that file size.
Requires two more free programs to work, (it's actually a batch file which uses them), but the price is right - the images need to be resized first before running the batch file over them.
Another EDIT: DOH! I just realised I already have a program on my computer that does this only it doesn't copy the EXIF info, (to expand: Analyzer copies EXIF data, however the Batch plugin loses it - I've just sent an email asking if he can implement it).
Image Analyzer with the Batch Plugin. Image Analyzer is free, the unrestricted Batch Plugin is Donationware - donate what you like and you'll get the version that doesn't add a small watermark to your pics, (I donated ages ago to have the ability to DeSkew a lot of pics - still use it occasionally because it can handle maths expressions in the batch files).
eg. To scale and save as you were after, the batch file is, (could probably do a lot of tweaking for max image quality, etc):
SkipNextIf(Width>Height)
goto(@ShortWidth)
SkipNextIf(Height<1001)
Resize(round(1000*(Width/Height)),1000,Pixel)
goto(@SaveIt)
@ShortWidth
SkipNextIf(Width<1001)
Resize(1000,round(1000*(Height/Width)),Pixel)
@SaveIt
SetJPEGQuality(100)
SetJPEGSizeLimit(1024000)