Multi channel amp advice

Hi all,
I have just moved into a house that has ceiling speakers installed.
Six in the living room (3 front and 3 rear), two in the dining room, two in the study, two in the workshop and two outside.
All cabled to a central point beneath the TV in the living room.

In the living room I have a flat screen TV with poor sound being fed by a Uverse DVR using HDMI.

The main thing I want to achieve is to feed the speakers in the living room with the audio from the DVR so that we dont have to have the TV cranked up to 70 to hear anything.

We currently dont have a DVD/Blueray player, receiver or any other hifi equipment.

What amp will I need to deal with my current and perhaps future requirements?
Would something like the Dayton Audio MA1240a be suitable?

What method would I use to feed it from the DVR?
Would I be able to power up all 6 speakers in the living room (I assume they were installed this way for a reason).

Many thanks.

Hi JD,
Many thanks for a very useful reply that makes a lot of sense.
I assume either a 6.1 or 7.1 AVR would do the job for the LR.

I have previously fed a pair of outside speakers connected directly to the zone 2 outputs of the AVR instead of going the pre out with amp route. Would I not be able to connect a 4-zone impedance matching speaker selector directly to the zone 2 output and then feed the other pairs of speakers around the house that way? I would then save on not needing another amp.

Thanks