Tivo IS the cable box. The main reason to get one is that it actually works, because lots of cable boxes out there barely do, particularly those from TW. Whether the DVR is essentially faulty, or that it lacks HDCP repeaters, etc. The UI is very nice, the remote is nice, streams lots of goodies, is remote programmable.
You don't pay a monthly fee to the cable company, so given enough time to make back the large initial outlay, you will be in the black at a certain point, probably will take a few years though. It will probably have OTA input, and I don't know that cable boxes ever have that. Though your TV prolly already has one.
So if your provider offers a box that works reasonably well, is not too expensive to rent, and that you don't care for streaming and/or already have other devices that do that for you, stick with what they give you. Tivo costs a lot at first. Even if it's a nicer rig than any other cable box I've ever played with, not even close.
edit: btw, at first glance, you seem to be too focused on the AVR/NAD. Personally, as a NAD amp owner, I'd shy away from their processing side. REGARDLESS, you need to consider speaker choices first and foremost, and after that personally I'd look at some of the recent open box and/or refurb Denon deals at this point. If you don't care for Audyssey (and I really do), I might consider Yamaha instead for their excellent track record. I have two Onkyos right now, myself, and unlike a lot of the FUD that is given out here, mine keep on chugging, I just recently opened up both to clean them, though they apparently didn't need to be. Main HT Onkyo was refurbed, close to half a decade right now already?