All Benchmark System Question

I would not recommend getting a combined streamer / DAC since if you wish to upgrade one you end up swapping the other. Provided you are serious about your pursuit. I think your current equipment confirms you are. Each component is a critical one to the system.

yes, you would control your streamer with your iPhone through your network. But the streamer itself would communicate through the Ethernet wire to your network. . 

You connect your streamer directly to your network, either by eternet cable or buy a wifi extender. You plug the extender next to your equipment and plug a short Ethernet cable into that. You can get a little extender that plugs into the wall like a wall wart. Then you use an app on your iPhone, or preferably iPad to control the streamer. I works incredibly well. Aurender has a great app that shows all your music… Qobuz, any you place on the streamer storage, and any that happens to be on your network storage. It does an amazing job of integrating all the music you have access to. It will cashe it so it can help make up for any short network latency. The better the streamer the more it makes up for network issues.

Definitely start with the source then. See if you can borrow one of the less expensive Aurender Streamers. The difference will be jaw dropping. Also try Qobuz streaming service… free for a month. I started digital streaming about 15 years ago… incrementally upgrading all components piece by piece from an iPod on both my headphone system and main system. I held off the longest on getting a dedicated streamer… it’s only spitting out bits, right? Wrong… it is the source… everything that follows is completely dependent and contingent on it. It is the key source like in an analog system… the TT, then phono stage, then preamp… etc. they all matter, but a noisy poor start equals highly amplified carefully crafted poor sounding stuff. I recommending at least as much as any other component. My streamer is about 20% more than most of the other components in my system components and well worth it! I got there incrementally so know the intermediate steps.

My digital end is now very comparable to my high end analog end.

In my experience you can venture a bit too far in the too detailed / analytical direction and that all recordings will sound better with better less analytical component(s) more musical. I would start at the signal source, if that is harsh and cold then everything else takes on that cast. For instance a high quality music streamer is going to sound leagues better than a PC. If the source is excellent then move to the DAC. But the key is not to look at this as a 20% of the recording problem... this is a whole system problem. There are bad recordings... sure... but it is easy to have a system that makes all recording sound good,.. just some are not as good as others.