I can answer any question you might have. Here's some basic info:
DirecTV is not renewing it's contract with TiVo, and has been installing their own DVR instead of TiVos for the last several months. DirecTiVos ARE still available (model R-10) if you ask, but you may need to shop around from several retailers. The TiVos are much better than the DirecTV DVR (model R-15) in ease-of-use, and since you are a TiVo owner already, I would recommend the TiVo.
Both DVRs have 2 DirecTV tuners, so they will need 2 lines from the dish to the DVR, one for each tuner. This allows you to record to shows at the same time (you can even do so while watching a third, previously-recorded show off the hard drive), or to record something and watch something else live. The TiVo *requires* a land-based phone line (no VOIP, cell phones, etc.) to set up, but since you have TiVo already, you're probably fine there.
In the past, multiple vendors made DirecTV receivers, but DirecTV has, over the last 18 months, terminated those licenses, and now all new DirecTV equipment is "DirecTV brand". This is because DirecTV is switching NEW CUSTOMER contracts from an equipment ownership business model to an equipment lease business model starting on 3/1/2006. Customers who activate on or after that date will be leasing their DTV receivers, just like DishNetwork has been doing for a long time and cable has been doing forever. This is good and bad: good because you no longer have to pay for a protection plan to cover a receiver that dies; that's included in the lease. Bad, because you can no longer get out of your programming commitment without paying a pro-rated cancellation fee by returning your receivers. Existing customers who own their equipment, or people who buy their own equipment anyway, will see no change to their current agreements.
The DirecTV R-10 has an 80GB drive, giving 70 hours of programming. The HD can be upgraded (to as large as 1 x 400GB or 2x250GB, the latter with some additional parts), but the R-10 cannot have its TiVo OS modified (read: hacked) like the previous non-DirecTV-brand units could. This may or may not be at all important to you. Some folks (like me) have hacked their TiVo software to turn on the USB ports and enable the networking drivers. While this does NOT give you TiVoToGo functionality, it does allow you to control the TiVo via web page, and possibly extract some the recorded shows with further hacks. To do this, you'd need to buy a used, non DTV-brand DirecTiVo. I have a Samsung SIR-S4080R (80GB) and a SIR-S4120R (120GB), which are both Series II TiVos like the R10, but don't have the additional chip on the motherboard that prevents TiVo OS hacks. You can buy these from eBay or from TiVoCommunity.com. In many cases, you can buy them pre-upgraded and hacked.
If you end up going with the non-TiVo R15, you should know that there will be some benefits to doing so. One of those is that these units will work with upcoming handheld playback units (ala Video iPod) and you'll be able to transfer shows from your R15 to it via the front-panel USB port. DirecTV announced partnerships with Microsoft and Intel to integrate DirecTV into Windows Media Center and Windows portable media players at CES last month, and you'll have to have an R15, or the upcoming Hi-Def HR-20, to do so.
As far as the dish; they'll install the right dish for the programming you order.
-Troy