Although there is nothing wrong with picking up a used TiVoHD, I would not be afraid to buy a Premiere for OTA use either. Both work well for OTA. As far as the antenna, I think Antenna Web.org is good so find specific antennas you think will work based on the recommendation and ask about those here, we may have experience. I am using a modified Eagle Aspen DTV2Buhf Directv 2-Bay UHF Antenna, I modified to pick up the one VHF station in Little Rock and it works great for me in my situation but probably wouldn't work for many others.
You are right to want additional sources and although I don't own an XBox 360, I do own the PS3, other disc players and Google TV for internet streaming access. I dropped DirecTV over 2 years ago and I am happy. After the purchase of a TiVo and antenna, your investment won't be small and it will take some time to recover it depending on how much you are saving but you will get there and in time be ahead. Most important advice I can give, get lifetime service if economics are the reason for the switch.
You are right to want additional sources and although I don't own an XBox 360, I do own the PS3, other disc players and Google TV for internet streaming access. I dropped DirecTV over 2 years ago and I am happy. After the purchase of a TiVo and antenna, your investment won't be small and it will take some time to recover it depending on how much you are saving but you will get there and in time be ahead. Most important advice I can give, get lifetime service if economics are the reason for the switch.