So what would you say is the best quality/ratio video format and settings that could be read by an ipad without decoding and third party app?
It's subjective. I don't know what's an acceptable clarity to you or what's an acceptable file size.
You'll see lots of recommendations for encoders and people will swear x is better than y but, through that all, handbrake has always held up and hasn't gone away. Personally, I'm a fan. It's also in the process of introducing h265 encoding which is relevant as recent iPads play h265 as a native codec with ios11. The main selling point of h265 - the successor to h264 - is that it can usually provide the same quality as h264 with a smaller file size. You'll also get hardware acceleration on the iPads native video player.
But before all that, it's worth clarifying the basics of video files. A video file is a
container that contains a
codec. People will often, understandably, mistake one for the other or don't know they're separate things.
The
container is equivalent to say, a phone. And a
codec is equivalent to a phone OS. So you could have a Samsung xblah21 and a OnePlus zblah31 with both running Android 7 as an OS with the same color, memory, cpu, etc.. People will mostly base their experience on what worked well and what didn't with Android 7, whether they know it or not. A few will say, I preferred the feel of the buttons on the side on the Samsung or, the OnePlus is available in my country more readily than Samsung, etc., but most views will be critiquing something about Android.
You can apply that analogy to video files. Some people will bicker about the
container, and sometimes that's important. As well as some players not playing certain
codecs, some players won't play certain
containers. But most of the critiquing is about the
codecs.
The
container can sometimes be obvious from the file extension, but not always. MKV is a container, Quicktime is a container (MOV), as well as AVI and MP4. These can all be using the same
codec and, if they are, the differences between them are far less varied. Mostly it will come down to whether the players you use can play the file type, subtle quirks between them (which can becomes less subtle for niche uses), and if they'll hold up in the long term.
Codecs are the meat of the video file and are by far the dominant factor about the clarity and file size of your video. h264 (MPEG-4 AVC) is a codec and the most popular today. It holds up well with clarity/file size ratio and the industry was pretty confident in it. So much so that it's one of the main codecs that manufacturers provide hardware acceleration for, which will usually improve battery life. There's been reluctance to move on but manufacturers are slowly going towards h265 (HEVC) and we're seeing a similar uptake in providing hardware acceleration for it, with the same benefits for the battery life.
I don't have an iPad but I believe it only hardware accelerates the h264 codec (and h265 in ios11 on newer models) in a Quicktime (mov) or MP4 container. I'm not even sure if it will actually play video files not in this format so perhaps hardware acceleration is to be expected if it will actually play the file at all. Somebody with an iPad can correct me on that.
Based on that, you want to make sure you're converting any video files into a Quicktime or MP4 container using a h264 or h265 codec. I've no idea what settings are satisfactory to you, as a I said at the start. But you could work off the idea of what's the max file size you'd be happy with. Say it's 800mb for a video and you know the video's one and a half hours long, you can do the math to figure out what to set for the average kbps box. That way, you'll know the file size that comes out and you can see if the quality's good enough at that level for you. I'll spare you the math to keep this wall of text from being even longer but as a barometer, an hour and a half movie at 800mb would need to be 1185kbps.
You'll never really have an opinion or knowledge of anything without trial and error so I suggest just a little patience and leave it running to do its thing when you go out. Otherwise you're just taking somebody else's word for it and could deviate way off what's useful or accurate.
Beware of the million video converting utilities out there that come and go. It's one industry where there's a myriad of people trying to make a quick buck when the utility that's proved the test of time and was often free is usually better. It's one of the reasons I'm recommending handbrake.
It's worth knowing that any conversion worsens the quality. If you know how bad of an idea it is to save a jpeg as a jpeg, it's the same with movies. But it's not so bad that it's unacceptable to many. It's really only an issue if you're going for really high quality and, on an iPad, you're likely not. With that in mind, check what the resolution of your iPad is and don't convert movies to a higher resolution than that. You'll just be using a larger filesize needlessly.
Finally, you haven't mentioned if you watch your iPad at home with the computer that's the source of these MKV files switched on. Transcoding is an option then, which is just converting and streaming live at the same time, without ever storing the file on your iPad. I'm not a fan but lots of people are. It's one of the main selling points of Plex, if you're familiar with it (and it may be worth looking into if the scenario I just mentioned is applicable to you).