I don't have an iPad, but the files I make work well on my iPhone 6s Plus. I primarily make them for viewing on my Apple TV's and on the web. Handbrake came out with an update a few months ago, but on the old version I used the Apple TV 3 preset and it worked well. That preset is still available under legacy settings.
With the current version I have just been using the "SuperHQ" preset. The only things I change there are in the interlace settings on the "Picture" tab, depending on my source material. For interlaced video (mostly old material like TV shows or home videos) then I use "Yadif" for Deinterlace with the default preset. If the source is not interlaced then I set Deinterlace to "off". In either case, I leave Deinterlace detection to "off" since I manually configure that. But really, if you aren't familiar with this kind of stuff I would just leave all that alone and let Handbrake decide what to do. None of this should have any effect on file size anyway AFAIK. I do not change any settings on the "Video" tab.
Now my goal is to make the highest quality video at reasonable size, so I haven't experimented much with the other presets. You can try the HQ, Fast and Very Fast settings to see how you like those. My results are probably not very relevant to what you're doing. Mostly I'm starting with ProRes422 files that are quite large. For example, I just converted a 10 minute 720p video that was originally 5.7gb. The Handbrake SuperHQ file was 645mb. When I convert standard definition DVD's that are typically 4gb I usually get files between 800mb to 1.5gb.
Sorry, that's about as much as I can help. Handbrake is really popular, so a little time with Google should point you in the right direction.