Built in SATA and space for at least one hard disk. A second SATA and space for an optical drive would be nice.
Room for a couple of expansion cards
And yes, I'd be prepared to pay thirty or forty quid for it. Frankly, I'd settle for an easily available board to make it ITX compatible.
You don't get SATA and PCI interfaces from a case! You're describing a different platform.
Are you aware that you can get an ITX format fanless Intel-x86 PC board with all you ask for, plus probably rather more CPU grunt, expandable RAM, etc. for £50ish? Gigabyte GA-J1800N-D2H. Built my home PC around this - a 100% solid-state PC, completely noiseless. Although to be fair this is around £200 by the time it's built into a full-blown PC, or around £100 for a bootable bare board.
More Pi-like, there's the CubieBoard series with SATA and more RAM than a Pi. I've not used one. https://en.wikipedia.org/wiki/Cubieboard
Cheapest linux system-in-a-box is a broadband router running OpenWRT or similar. I have a £17 Trendnet router (check the OpenWRT hardware compatibility list). Inside is a five-port fully VLAN-capable switch and double the RAM that most of them boast. Slightly dearer ones also have USB ports. Others cost under £10 for CPU, Lan and Wireless. Main drawback with routers is (usually) very small RAM capacity.