Component recommendations: best bang for buck.

I know avlee said that you can ignore 4K processing and run all your sources to the TV (I'm assuming that you would just use a digital coax or toslink connected to a AVR/processor for the audio).  The problem here is that you will NOT get any of the hi-res bluray audio formats (TrueHD, DTS-HD MA, Dolby Digital Plus).  Audio through coax/toslink will automatically be down-converted to the old school compressed Dolby Digital / DTS formats.  If you want hi-res bluray audio, you are going to have to connect everything through your AVR/processor using HDMI cables.

Second question, before I move on.  You keep brining up "integrated amplifier" options.  This leads me to believe that you want to connect some analog audio sources (such as turntable or DAC) directly to the integrated amp to use as a dedicated 2-channel audio system.  Please let us know if this is your intention.  This is fine if you want to do this.  It would mean that any AVR or HT Processor would NOT be used for regular 2 channel audio.  You can still merge the two together (using the integrated amp as the "amplifier" for left and right channels).

If you are intending on running all audio sources (both analog and digital)through the AVR/processor, then you are better off getting a regular amp and NOT an "integrated amplifier".

HT Processors:

Marantz 8802a - (if you choose this, make sure to get the 8802a model. The original 8802 does not support HDCP2.2). Based on your budget and everything you need to get (speakers, etc.), I would probably recommend this. It is an excellent internal architecture design with a very large power supply. The DAC I/V stage is op amps, but has fully discrete audio output stages. It supports all the latest standards (4K, etc.) and is the most cost effective of your selection. The sonic signature is slightly on the warm side and just a little bit laid back, but all the detail is still there. It’s typically $2500 used, but there are some new ones on ebay for around $3k.

Krell Foundation 4K - This is another excellent choice, but completely different than the Marantz. The Krell is going to have very high resolution with a lot of detail and impact (for HT it is an excellent choice, but also excellent for music). Krell is still doing updates to this product. Typically runs for about $4,000 to $5,000 used. I own the Krell S1200U, which is awesome and better than the Foundation (S1200 has fully discrete Class A audio stages where Foundation uses op amps), but the S1200 does not support 4K.

McIntosh MX122/160 - (I’m assuming you mean the 122/160 because these are the only models that support 4K). Many love the McIntosh processors. They have the "McIntosh" warm sonic signature and the front panel is just beautiful. The internal architecture is excellent. I looked at the Mac and it was on my list, but I did not want a warm sound and I was concerned about all the bugs that appear in the processors which McIntosh never fixes (just start searching in the Audio Aficionado forum). The 122/160 are going to be in the $6,000-10,000 range as well. The older 121/150 models are cheaper used, but they do not support 4K. If you wanted this type of sonic signature, I would just go with the Marantz 8802a as it is an excellent product. Marantz continues to support this model.

ARCAM - I don’t know much about them, but I have read a little bit. They seem to be excellent with a highly detailed sound and a huge amount of impact (great for home theater). You should research more if you are serious about this choice. Personally, I would probably go with the Krell unless you wanted all the extra Dolby Atmos channels. For me, a high-end 5.1 channel system is better than an average 11.1 channel system.

My one question (among many others) is would my TV/display benefit from the "additional" video processing of the AVR unit vs. plugging the HDMI directly into the TV (I have the latest 4k TV from LG)

It depends.  Sometimes the video processor in the AVR / HR Processor is better than what is in the TV.  Sometimes it is not.  Usually, there is an option to disable any "video processing" in the AVR/Processor and just "pass-through" the video.  I would not worry about this question that much.