A mini PC could certainly work! If you're willing to go ebay, I'd recommend any of these Lenovo Thinkcentre SFF PCs:
1-2x m.2 slots, 1x 2.5" slot, and some can accommodate a half-height PCI-E card in place of the 2.5" slot. Presumably, you'd want to go Intel for QSV
Wow, that's a great deal. I currently have two: one w/ a dual 1-gbe NIC for opnsense and another for proxmox