I am looking for a single board computer with 2x1 GBit ethernet ports, on board.
Should come with SATA and/or USB 3.
Either x86 or ARM is ok, as long as it runs Linux.
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There's apparently NUC style passively cooled machines meant for displays that would work.
Discourse uses something very similar internally
I've been toying with buying one of these and it probably ticks off most of your boxes - intel ethernet, and 4 ports (realtek's a pain). I've run linux on a very similar platform. With the right variant, you got USB 3.0 + 2.5 inch drives, or msata.
I ended up picking up a slightly fancier model but you can get a 2 port model with a j 1800 or 1900, ram and storage for about us $150 upwards. It's fairly robust, has Intel lan adaptors (which I find better than realtek) and basic video outputs.
So yeah, they exist and for not much money.
There is the x86 ODROID-H2 SBC which comes with 2 x 1 GBit ethernet, 2 x SATA, 2 x USB 3.0 (4 USB ports in total), 1 x M.2 NVMe and more.
As of 2018-12, it's sold for $ 111.
It's based on the Intel Celeron J4105 platform (CPU is soldered) and has 2 empty DDR4 SO-DIMM slots.
When using the SATA ports you need special SATA power cables.