What about a thin client? You could find a very nice HP one with a respectable amount of expand-ability that ran X86_64 software for around $35. Then put your system/ecosystem together yourself. Maybe there is already one out there.
Unless you are already wedded to one, I would stay away from the (aforementioned) kind of devices. I wouldn't pay for one, thats for sure. Since they mine peoples information, IMHO, they should pay you.
As far as free standing, you can find an HP t620 quad core thin client for atound $25-30 and if you are smart, even find one with the stand and specially built power supply. They use an internal SSD. I dont know if you can install a standard SATA SSD in them, hey have internal space for a very small SSD. But they have gigabit Ethernet, can be expanded up to at least 8 gigs, quite possibly 32 gigs, and the t620 plus or t730 both can hold an internal PCIe NIC or I think internal HD. (they have space for a very small PCIe card) But those two models are significantly more expensive on the resale market. They have some very small thin clients that sell for very cheap, possibly $20 that might suit you particularly well, but there are lots of variables involved. These tiny machines were meant as desktop substitutes for businesses whose employees spent most of their time interacting with a single web application and on the telephone. They have the capability to do most basic things and they are cheap. They would be good for carputers too.
Used they cost less than a new Raspberry Pi and have more power. But they take more power too. Typically 19v at 3 amps.