Regarding monitors: It’s better to use fewer large screens than many small screens. So, in your case, I assume that two or three 4k monitors should be sufficient. There are graphics cards that support up to three monitors. If you don’t plan to play games, a card from the lower end will be definitely sufficient.
If you absolutely need more monitors than you can get ports on a single graphics card, I recommend you go with Nvidia. The Nvidia driver supports multiple GPUs at once with X.org. You can use the nvidia-settings tool, it lists the various GPUs in the system and enables you to assign them to virtual screens, which in turn can be arranged for the X.org display. This is very easy and intuitive to use. If you buy multiple graphics cards, an AMD CPU might be preferable over an Intel CPU, because recent AMD processors have more PCI lanes, which can become an important factor when using multiple GPUs.
Regarding mainboards, I made good experience with ASUS boards. Most of them are marketed as “gaming boards” (under the “ROG” label), but you can just ignore this. They usually work fine for standard desktop systems, even if you don’t play games.
Just as an example, my current system is based on an “Asus ROG CROSSHAIR VII HERO X470” with an AMD Ryzen7 2700 processor, 32 GB RAM, and an Nvidia 1030 graphics card (low power consumption – this one has only two ports, but there are models that support three 4k monitors). That system is about 2 years old, so today you can probably get somewhat better successor models. For I/O performance I use a Samsung 970 PRO NVMe SSD – I never had anything that came close to this beast, speed-wise. Depending on what kind of VM you plan to run (and how many), 64 GB RAM might be preferable.
As far as Gigabit Ethernet is concerned – Those are standard for quite some time. Even on most low-end boards you get Gigabyt Ethernet; only some embedded systems for special purposes come with FastEthernet (100 Mbps). Meanwhile, some high-end mainboards even provide 10Gbit Ethernet.
PS: When you max out the RAM slots on a mainboard, be sure to get quality RAM. It’s best to consult the vendor’s compatibility list, so you get modules that are proven to work. That’s important because when you approach the mainboard’s limit of the amount of RAM, the boards are usually more picky about the RAM timings.
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