what are all the pieces of hardware and software necessary to have dvr function with an OTA antenna?

What I would use would be a lower powered PC to use as a Home Theater PC (HTPC). Pretty much any dual-core processor would work for your. Installed in the PC (or on the network) you will need some type of TV Tuner device. Since you're wanting to DVR Free OTA broadcasts, you will need a TV Tuner with at least one ATSC (digital) Tuner. Just make sure the one you opt for has drivers for whichever operating system you intend to use. You'll also probably want a large storage drive to store your recorded shows.

The HTPC can run either Windows or some versions of Linux. It will also need to have some sort of Media Center software. Since Microsoft killed off Windows Media Center with the release of Windows 10, one other popular software package is Kodi, which runs on either Windows or Linux. The system will need to have internet access in order to download the latest Electronic Programming Guide (EPG).

Other than that, about the only thing missing would be a Media Center Remote. If I were to build a new rig right now, I'd probably look at:

Dual Core Processor w/on-board graphics
8GB RAM
Large Storage Space
ATSC TV Tuner Device
Antenna
Media Center Remote Control
Blu-Ray Drive (optional)

Operating System (Windows/Linux)
Media Center software (Kodi)
Blu-Ray Software package (required for Blu-Ray playback)

-Wolf sends