D-Tivo's will work on any of the satellite positions, so it makes no difference the dish that you have. But, you DO need to have 2 feedlines from your dish to the receiver to make BOTH tuners work. But since you are already using 3 standard receivers, you should have 1 extra port available on your dish/switch for this - you just need to run the coax. And, if for some reason you CANNOT get another coax to the Tivo, it'll still work fine with only 1 feed, but you won't be able to watch/record 2 different shows at once. (But you'll want to do this anyway, I guarantee it...)
Besides the fact that the only D-Tivo unit's currently made are the D* made R10 units, any of the previous brands that may still be out there are EXACTLY the same. (ONLY difference is the shape of the receiver itself) You can buy strictly on price, but they are pretty much going for $99. (although, I did decide to pick up one of the last Hughes HDVR-2 units that was left at my local BB last night - I had a 10% coupon, as well as a $10 rewards coupon, & since you can do feature hacks easier on these, thought what the helll, I'd get it) My two series ones are NOT going to be updated with the newer features & I thought I'd go for the speedier one.
For your purposes, the R10 will work just fine for you.