Use https://linux-hardware.org/ to check stuff. Ask questions with the links if you do not understand the reports. Everything you can build with has a proprietary bootloader, even the System76 stuff is proprietary.

It’s not so much about motherboard brand as it is about the chips used on any given model. For example, ASUS makes some boards with Intel i225-v ethernet, and others with Realtek RTL822x ethernet. The Intel chip is notorious for stability problems (on all operating systems), and although I think the linux drivers eventually managed to work around them, the boards with the Realtek chip avoided those problems entirely.

With that in mind, I suggest you look at a few key chips used on any board you’re considering, and search linux forums for problem reports with their model numbers. In particular:

• Ethernet
• Wi-Fi
• Audio

Sometimes you can find comparison charts for such things, like this one for socket AM5 boards

Also, it’s nice to have a board that can update its own BIOS from a flash drive, rather than requiring a Windows program to do it.

Check for WiFi and Bluetooth drivers compatibility first. Every x86_64 motherboard should work with Linux well, as in, it will boot and all USB/PCI Express/SATA ports will work. What you should care are peripherals soldered onto the motherboard, like WiFi, Bluetooth, extra Ethernet ports, ten years ago I would say soundcards but nowadays all integrated soundcards are supported, some motherboards have strange ports like Firewire which might not be supported, integrated videocards are now soldered directly onto CPU and not on motherboards like before so HDMI ports should all work on any motherboard.

And yes, as the other commenter said, check that firmware update does not require some Windows program, and could be done only with USB drive and selecting some option in the BIOS/UEFI menu.