I have recently received a first gen iPad Mini. My experience with Handbrake is limited. Can anyone recommendation what settings to use on Handbrake to convert HD source ( mostly 1280 x 720 ) to watch on the smaller 1024 x 768 screen without losing more quality than already lost from the smaller resolution, but also without making the files bigger than they have to be. I would also like the video to take up the whole screen without borders ( I don't mind if it stretches a bit ).
As I've got an iPad mini myself I would definately recommend you the Apple TV preset.
Your iPad mini does not have retina display, nor does mine (first gen.) and converting to Apple TV format is great (720p instead of 1080p) and results in a smaller size file than iPad preset does.
As usual, the answer is “it depends” because viewing quality is subjective, space is less of an issue on a 64GB iPad than a 16GB iPad, and a desire to use Airplay means you need a higher resolution file.
Your best bet is just to start with the iPad preset and start increasing the Constant Quality/RF factor until you don’t like the quality.