1) DVR from cable company. Problems: I've gotten anecdotal information that these DVR's have poorly designed UI's and tend to be somewhat flaky (worse than Windows). Also, they are a closed system, I can't move the recording to a mobile device for portable viewing.
At least in my experience with Comcast DVRs, yes they are flaky, the interface is poor, the fast forwarding sucks, and it has had problems with just magically losing all recordings twice in the two years I used it.
2) PC + HD ATSC / Clear-QAM tuner card - this gives me the ability to record over the air broadcasts and cable channels that support Clear-QAM (which is a fairly small subset of cable channels).
Works well, although I'd recommend something like the HDHomerun (dual clear-QAM tuner box that plugs into your home network). At least where I am, I get pretty much everything on basic cable in 480p, and then the OTA channels plus a few others in either 720p or 1080i.
Beware that Comcast likes to leave their QAM frequencies undocumented and likes to map them to different channels periodically. So if you're using MythTV you'll want some familiarity with the database, particularly the channels and dtv_multiplex tables. That said, with the switchover to digital, I no longer have the ability to record analog cable and you may find the same problem in upcoming months. In particular, in my area, Comcast switched QAM frequencies last month (again) and is now using some of the area formerly allocated to analog.
3) PC + HD Tuner Card + Cable Card - does anyone make one of these? Anyone have any experience with this?
Tivo is your easiest solution. Windows Media Center will support a CableCard but with some tweaking required (good writeup here: http://hd.engadget.com/2009/05/12/how-to-install-a-cablecard-tuner-in-your-diy-media-center/)
I don't know of a way to get MythTV working with a cable card and it seems rather unlikely because it is a hardware / vendor lock-in.