Apple TV connection to DVR

Can/should I connect Apple TV (3rd gen) to my AVR via ethernet (then to my Samsung S90C), or do I connect Apple TV directly to the Samsung TV bypassing the AVR?

Not ethernet, but HDMI. Either order of setup is possible. The ‘best way’ depends on the capabilities of each device. The middle one should be capable of doing passthrough of either video or audio. An older/lower end AVR might not support 4K HDR passthrough; an older/lower end TV might not support PCM 7.1 or Dolby Atmos MAT passthrough.

An AVR will typically have more HDMI inputs than a TV, which can be convenient to have multiple devices permanently plugged in. That is how I have it: Apple TV →[HDMI]→ AVR ⇄[HDMI (e)ARC]⇄ TV.

Also is Cat 6 enough, or should I use higher?

Ethernet Cat 5e or later is recommended for wired networking. Higher version is more future proof (and better shielding from interference).

Ethernet is used for network input of content, not for communication between Apple TV, AVR, TV.

Network input for Apple TV is necessary (ethernet or Wi-Fi). Network input to the AVR might be used for other functions (internet radio, updates). Network input to the TV might be used for other functions (smart apps, updates).

For HDMI 2.0 ports, use cables rated for 18 Gbps or higher. 48 Gbps rated cables are recommended for connections between two HDMI 2.1 ports.

If one of the HDMI ports on the TV is labeled as “eARC”, then it likely supports PCM Multichannel and Dolby Atmos passthrough. If you try it, then Apple TV will show what it can detect for supported features. Apple TV will hide features that it can’t detect as supported. Regular ARC will have limited bandwidth in the return channel direction, and wouldn’t support PCM Multichannel or Dolby Atmos in Dolby MAT format in that direction. Instead regular ARC supports Dolby Digital 5.1 and lesser discreet audio.

Samsung TVs do not support video in Dolby Vision format on any model, as a manufacturer’s choice. This has no influence on audio. Instead of Dolby Vision, you may enjoy video in 4K, in SDR, HDR10, or HDR10+ format. HDR10+ passthrough via AVR will need support on the AVR as well; I think this is available for select 2020 or later models AVR.

I hope that makes sense.

To get all the video features that your TV supports, and all the audio features that your AVR supports, I would recommend: Apple TV →[HDMI]→ TV ⇄[HDMI (e)ARC]⇄ AVR for you, as the TV is newer than that AVR, and has wider support.

Most HDMI is from input to output; directional. eARC is Enhanced Audio Return Channel. These special ports support sending audio in the other direction as well. Data can go both ways through these HDMI ports, not just into the TV, but for audio also from the TV. That is what the double arrow notation was used for. So use the (e)ARC ports for the connection between the TV and the AVR (or any audio system). Connect other devices to other ports.

You’re welcome. Enjoy the Apple TV box and its content.