Lenovo M720q Tiny - Pentium Gold G5400T, 4GB DDR4, no HDD, with PSU - $149.99

Yes, it is technically possible to add a NIC to these systems, but you will need a riser card as well as the NIC. And as an added bonus, the port on the motherboard isn’t a standard PCI-E port, so you have to use Lenovo’s proprietary adapter, part number 01AJ902. DHole mentioned it in his build log post here: Lenovo M720Q - This thing is RAD! The riser is hard to find and very expensive.