MP4Tools Proper Audio Selection?

In general, you will absolutely need the AAC audio track (may be stereo, some people downmix AC3 surround into Dolby ProLogic in this track), for audio output across Apple-board (incl all iOS devices).
You may want to include AC3 5.1 surround audio track that appleTV knows to pass through to surround receiver or TV set via digital outputs (HDMI or optical TOSLINK).
Now, that being said, if your source does already have AC3 track (as seen on your pic), you don't need to re-encode it, you can just check the pass-through option. This makes the tool simply copy the bytes from source file to destination file, without any processing. Meaning the bitrate will remain the same.
You will need to convert all other flavors of surround tracks (mostly DTS, occasionally also AAC 5.1) into AC3 5.1 for aTV playback, that's what the bottom-most checkbox is for.
As DVD or BD-ripped sources rarely don't contain AAC audio tracks, you will almost always need to select this option. As for bitrate - you can leave it a tad less than your source, as AAC is supposed to be more efficient codec (they say 192kbps AAC is perceptionally equal to 256kbps MP3). You will not gain anything if you encode into higher bitrate, than your source was. You just waste space.
AC3 is normally found in 338-640kbps on the source (640k being it's max by definition), so I usually encode this into 192k or 256k AAC. If the source is in DTS, then higher.
IMHO the new MP4Tool also highlights incompatible selections in red.
And yes, AC3 6-channel is the same as 5.1 (5+1=6, right)!

benh911f said:

So you're saying I could just leave the passthrough checked, and AAC 2-channel checked, and I'll be good to go? File will be able to play across iOS devices, and provide 5.1 audio through a setup connected to ATV?

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Precisely!

benh911f said:

For a file that has ac3 6 channel like this one, selecting ac3 5.1 would be redundant, correct?

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Yes, AFAIK it would create you another AC3 5.1 track from the original. You will be able to select and play back that track on aTV as well, but what's the point?

benh911f said:

Finally, always choose AC3 5.1 over AAC 5.1?

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So it is. AAC5.1 can currently be played back only on Macs in Apple ecosystem, not on iOS. Even then I know of no external decoders or AV receivers that would take AAC 5.1 digital stream and play it back. That world has moved towards DTS and Dolby lossless codecs.
So basically, as I understand it, people use Sound cards to decode it and then feed those 6 channels as analog line in into a multichannel amp.