A prepro is literally "preamp + processor". So it decodes audio formats and does the DAC step. Atmos is available via BluRay and also via various streaming services(Vudu, Netflix in a compressed form, etc).
Height channels are literally what they sound like, sound channels that are meant to be above you, either ceiling or high-wall mounted(there are various specifications for Atmos and Auro3D). They are one of the major benefits of the new sound formats although not the only one.
If you can't decode those formats, you still get 7.1 or 5.1 surround, typically.
We haven't seen any AVRs that measure particularly well, but the
Denon ones seem to be pretty good as long as you don't exceed 1.5V output. That's an annoying limitation, but it is what it is. You can spend $4000 on the Monoprice HTP-1 and get ~5db more SINAD, but it still has voltage limitations. Audyssey XT32 is pretty good, although allegedly not quite as good as Dirac, but better than the other "cheap" AVR competitors RoomEQ. And RoomEQ is very important.
We have only seen measurements of
one Essence product, but it turned out pretty well, so maybe the
Essence Evolve 8 channel HDMI DAC is good too. Buy one and send it to Amir for measurement! That's another direction you could go, but if you do, you need to provide your own amplifier and room EQ if desired. A cheap HDMI switch would take care of the switching need. But that is more complexity and cost even if the DAC itself is only $300.
I can't recommend any set of products in particular, it really just depends on your budget, level of technical knowledge, and tolerance for defects, since Amir has yet to review any HDMI AVR or DAC and give it a stellar grade. They've all got issues. You have to do your own research and make your own decisions.