There are a few considerations here that others have touched on but I want to lay it out a little more cleanly hopefully.

First and foremost, you have to subscribe to the channels that contain the programing you want to watch from Comcast. For example, if you just have basic cable, a TiVo won't get you HBO, you have to get HBO from Comcast to start.

Second, when you buy a TiVo, unless it is an odd duckling with lifetime service, it will not have the service/subscription component required to let it operate correctly. This costs about $20/month, give or take, depending how long you lock in for. Any new TiVo (series 2 or higher) will connect to this service via ethernet, no phone required.

Third, most Comcast premium cable channels these days are encrypted. This means that you will most likely need a cable card compatible TiVo, (required if you want HD). I am not sure how you get your cable right now, but my guess is you probably plug it straight into your TV. This CableCard will cost extra to rent each month from Comcast ($2-8/month).

This leads me to my final point as ScottC alluded to, my guess is the best bet is to go the cable company DVR route (ie a cable company set-top box that records shows). It is probably the most straightforward option, you don't have to mess with CableCards, you don't have to worry about another bill from TiVo and if something is not working there is only one number you have to call (although you would have to talk to Comcast, so I am not so sure that is the best consolation). The price is very competitive with the cost of the TiVo service and I wouldn't be surprised if it is even cheaper. Plus you would get video on demand built right in (not available except on the latest TiVo boxes).