I am surprised at some of the comments you have received about buying DVR/PVRs.
We have not found any current-production units with ATSC tuners for quite a
while. When my last unit died, I decided to build one. In the end, however,
instead of building an HTPC, I decided to do my recording on my desktop.

Your first need is going to be a tuner. I strongly recommend the HomeRun
network-based tuner. In fact, we are strongly considering getting a second one
so we have the option of recording or watching live OTA TV on four channels.

For your application, I think MythTV and MythArchive will meet your needs quite
well. MythBuntu is a pre-packaged release with Ubuntu and MythTV ready to go.
That said, I have not had any luck getting other MythTV frontends on the network
to pull from the backend on my desktop.

I have not tried burning shows to DVD, but MythArchive appears to be the app for
that.