Amp recommendation and setup advice please

FOR TV SYSTEM:

To connect satellite to Audio-GD:  Blue Jean Cable Beldon 1694A – 6 feet. I always recommend 6 feet even if the satellite receiver is right next to the DAC. A digital cable that is too short will have signal reflections internally and will smear the sound.

To connect Audio-GD to AirMotivs: you could pick one of the gold-plated Audioquest cables, such as Tower / Evergreen / Golden Gate / Big Sur.  It depends on how much you want to spend on your TV setup.  The more expensive Audioquest cables have better copper conductors and the high-end ones have a NDS electric shield.  The Airmotiv speakers are likely to be placed further away from the Audio-GD so the cables are likely to be 6-9 feet long (or 2-3 meters).  These Audioquest are probably what I would recommend because longer RCA cables will increase the cost.  It’s not worth it to get something like Wire World Eclipse 7 for this TV system (which would be $700 USD for 2 meters)

FOR YOUR MAIN TURNTABLE SYSTEM:

To connect an iPhone/iPod, you will need an Apple Lighting to USB camera adapter and then a normal USB cable:

https://www.apple.com/shop/product/MD821AM/A/lightning-to-usb-camera-adapter

Keep in mind that this only supports the latest generation iPod (iPod Touch 5th/6th generation).  That page has a "compatability" section that shows the iPhone/iPad/iPod devices that are supported.  It would connect like this:

iPhone ==> Lightning-to-usb-adapter ==> normal USB cable ==> Gustard DAC USB input

I have read that some DACs do not play well with iphone iOS in recent updates.  You can google around if you are interested. For laptop, you just need to connect the laptop directly to the DAC with a normal USB cable (6 foot length of course).  In fact, you can just unplug/plug the same cable between your laptop and your iPhone/iPod.

Probably the best way to play music on the DAC is just use a laptop with media player software such as JRiver or other.  This will also allow you to play hi-res and DSD files to the Gustard DAC.

You can get better more expensive USB cables if you want, but to start out I would just use the basic cheap USB cable and see how you feel.  The better ones are made from silver/silver-plated conductors and they charge/discharge electrical signals faster which is more accurate for the high-speed digital signal.

To connect the rest of your sources to the Hegel, you will either need “single-ended” RCA or “balanced” XLR cables.  I will always recommend going with XLR if you can.  For example if you bought the Hegel and the Gustard, you could connect them using XLR interconnect cables.

The Hegel integrated has one set of XLR inputs (some integrateds, like the Arcam, do not have XLR inputs at all).  If you look at the Gustard DAC and the PS Audio Nuwave phono preamp, they both have XLR outputs, so you would have to decide which one got to use the XLR inputs on the Hegel.  You can use RCA cables for the other device.  Since you said that you only “occasionally” listen to digital music, maybe the better choice would be to put RCA on the Gustard DAC (unless you bought a phono preamp that did not use XLR).

So:

Laptop ==> USB Cable ==> Gustard DAC ==>  RCA/XLR Cable ==> Hegel

Turntable ==> RCA cable ==> phono preamp ==>  RCA/XLR Cable ==> Hegel

There are a ton of different RCA/XLR cables and tons of different opinions.  I generally avoid silver/silver-plated conductors for audio interconnects because I have found silver will tend to push upper mids/highs and be lean on bass.  It also imparts an artificial character to the sound (making it less real or natural).  There are many who love silver and silver cables could be good in some systems.  They would not be good in this system.  That being said, the Wire World silver-clad plugs are really not that bad and they do not forcibly introduce so much of that “silver” sound.

So, my recommendations are the same for either RCA or XLR cables (big surprise):

Less expensive gold-plated Audioquest cables, such as Tower / Evergreen / Golden Gate / Big Sur

More Expensive Wire World Eclipse 7 

The Eclipse 7 also makes an excellent cable for your turntable, unless the turntable already has a cable built into it).  The Wire World will have more resolution in the sound (better details / attack) and will likely have tighter and punchier bass.  It is significantly more expensive, so it entirely depends on your budget.  It is perfectly fine to mix Audioquest and Wire World cables in your system, or different models of Audioquest.  Once again, it all depends on your budget.

You will also need speaker cables to connect the Hegel to speakers.  You can start out with normal 12awg stranded Oxygen Free Copper (OFC) speaker wire if you want.  This stuff is extremely cheap, like 50 feet for less than $20.  It’s really not that bad, but better speaker cable will definitely sound better.  If you were interested, I would start looking at the Audioquest Rocket 33 / Rocket 44+ / Rocket 88.  You can sometimes get used Audioquest speaker cable, but I would make sure it does not have any silver elements (like silver-plated connectors).

If you got the Monitor Silver 10 speakers, try to look for a speaker cable that has “bi-wire” on one end so that you don’t have to use a jumper.  On the Audioquest Bi-Wire, make sure the high-frequency connectors are connected to the top binding posts.  The Audioqest speaker cable uses variable gauge solid-core conductors.  It will use larger gauge wire for bass and smaller gauge wire for mid/tweeter.

You should probably read this:

https://www.musicservertips.com/how-to-articles/iphone-digital-audio-output/

It appears that iPhone/iPod will not allow digital connection with some DACs.  You can try this with the Gustard, but honestly I think the best solution would be a laptop or desktop running media software such as JRiver.  JRiver has an excellent app (JRemote) that you can install on iPhone/iPad to remote control the JRiver on the computer (as long as you have a wireless computer network).  With JRemote you can view the music library in JRiver and play anything.

So, laptop/desktop is best solution (as I said you can always try the Lightning USB with Gustard).  Desktop will have a much better power supply and a better USB circuit.  Desktop computer is a LOT bigger and requires external monitor, but you can get a really good USB card to connect to the DAC, such as the SOTM, PPA (Paul Pang) or JCAT:

https://www.computeraudiophile.com/forums/topic/29199-would-you-recomemnd-an-audiophile-usb-card/

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I thought of another thing.  If you really wanted to use XLR cable for both DAC and phono preamp, you would have to get a separate preamp and amplifier (instead of an integrated).  Some preamps will XLR inputs for two sources (though many will only have one or none).  This will drive the cost up a lot more and you will also need another XLR cable between preamp/amp.  I think we are already way over the $5,000 USD point with the system we are discussion.  Doing a separate preamp/amp could potentially push the cost up to the $8,000-9,000 point.  As you said, since you only "occasionally" listen to digital music, it may not be worth it.  The Wire World RCA cables for Gustard will still be very excellent (unless your phono preamp doesn't use XLR).

The SOTM would probably be best if you used the stock computer power supply, with the JCAT being second. The Paul Pang really needs an external linear power supply, but it is likely to be the best if you use a linear power supply.

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Please note that I am going to extremes here.  In your situation, I would just start out using a basic laptop for digital music to the Gustard -- you may be perfectly happy with this.  If you feel this sounds "weak" or "grainy" or "dirty", you can always upgrade to a desktop and/or USB card in the future.