If it has to be a Single Board Computer:
I have an Udoo Bolt Gear which runs Qubes OS 4.1 very smoothly. This one may fit into your budget, but you have to keep in mind, that you’ll have to buy SO-DIMM RAM and M.2 SSD seperately.
Some downsides:
- Last time I tried Qubes OS 4.0 did not work,
- It has no PS/2 ports, which means that you had to rely on USB Input Devices, which have some risks attached to them.
- As far as I know Anti Evil Maid needs a TPM 1.2 with the Intel TXT Engine, which that Board does not have.
Even running many Qubes simultaneously, I never experienced larger CPU-/ Memory-/ IO-bottlenecks; so it would be more than fine for that use case.