If you want HDTV, then you will need another DirecTV receiver which supports HDTV, and you will need an oval satellite dish with dual LNB installed. You can buy all required products at
OrbitSat.
Also if you can receive over the air (OTA) HDTV signals, then you also need a separate antenna to pick up those local HDTV channels. You can find out if HDTV is available in your area by entering your zip code at
AntennaWeb.
Now for the TiVo part. You would need another TiVo, but it won't record in high definition

. It should still record standard definition as long as the DirecTV receiver is set to 480i output.
Total cost with HDTV support will not be cheap, but once you see a high definition picture it will be worth the price.