Yes, you can get used server hardware and use that. You can find very affordable servers in the 5-10 year range, and tailor it to your specific needs. Many of the cheap servers come in a barebones configuration, and may not include cpu, memory, hard drives, hard drive caddies, network cards, raid cards, and other hardware. So be on the lookout or be ready to customize the server to your needs.
The thing to keep in mind for unraid when it comes to older servers is your going to want the host bus adapters for SAS and not the RAID cards. You don't want to present the the drives in a