You will see no real benefit with the 2gb ati 5570 vs the 1gb ati 5570. The most intensive games on the market such as Crysis and Metro 2033 do not use more than 1 gb of memory. The memory also won't be a bottleneck in the future for future games for the amount of calulations units the graphic card has won't be able to process 2gbs of textures and polygons. Don't take my word on it read this review which compares the 5870 1gb vs the 5870 2gb. Note that the 5870 is 4 times faster than the card in the hp above and also note that the monitor resolution he used is double your intended tv, and even in those situations the 2gb provided no benefit over the 1gb of memory. In your situations it would be even less of a factor for you using a lower demanding monitor and a card who has less calculation units thus it needs less of a buffer for those calculation units to be properly fed.
http://www.anandtech.com/show/3621/amds-radeon-hd-5870-eyefinity-6-edition-reviewed/9

I repeat again do not get the 6 core, get the i7 930. Save the money for you are just throwing it away, a 5% real world performance increase is not worth spending $880 more dollars, you won't even notice it. Use that money on the ipad purchase, use it for a great night out, put it in a savings account/bond/mutual fund to spend on your next computer. Spending $880 more on 5% makes you a sucker.
Here is what I would recommend based off what you have given so far.

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Price $2,169.99* Instant rebate
-$350.00
Mail-in rebate
-$0.00
________________________________________
Total:
$1,819.99

• Genuine Windows 7 Home Premium 64-bit
• • Intel(R) Core(TM) i7-930 quad-core [2.8GHz, 1MB L2 + 8MB shared L3 cache]
• • 12GB DDR3-1066MHz SDRAM [6 DIMMs]
• • 160GB solid state drive
• • 1TB 7200 rpm SATA 3Gb/s hard drive
• • Microsoft Office Starter 2010
• • Norton Internet Security(TM) 2010 - 15 month
• • 1GB ATI Radeon HD 5570 [DVI,HDMI, DP, VGA adapter]
• • No speakers
• • Blu-ray player & Lightscribe SuperMulti DVD burner
• • Premium Wireless-N LAN card and Bluetooth(R )
• • 15-in-1 memory card reader, 1 USB, 1394, audio, with USB 3.0 card
• • No TV Tuner
• • Integrated sound
• • HP USB keyboard and optical mouse

I would recommend taking off the 16gbs of memory and doing 12gb instead, this way you use tri channel instead of dual channel and you will not need more than 12gb of memory. I am more of a power user than you and I have a similar computer (i7 920, 12gb of memory, 64 gb SSD, way too many harddrives for a I am a media whore, ATI 4890, blu ray player and dvd burner) and I have never seen my memory use pass the 6gb mark (part of this is due to the fact of legacy software some software can't use more than 2gbs of memory unless they use a software flag and due to the fact people want to make software 32bit compatible so it works with all operating systems [32 or 64 bit] than an individual program won't use more than 4gbs of memory due to the fact it won't work on 32bit.)
I also recommend doing i7 930 instead of the 980x, trust me you are wasting money getting the 980x. Next year they will have a processor that costs 300 instead of 1000 that will beat the 980x and it will be a quad core instead of a hex core so you will see better real world performance, save your money.
The 5570 1gb is a good video card, my 4890 is a better card (about twice as faster due to having more calculation units) and hp in their prebuilt allows you to have better video cards but it appears they won't let you choose something better like the ati 5770 (about twice as fast) on their online order. That said the 5570 is more than enough to play Napolean Total War and the older games in the Total War franchise, faster cards also have the unfortunate side effect of generating more heat and being louder. In addition the 5570 is a faster video card than the one in an xbox 360 or a ps3 as well this computer having a better cpu and memory so anything that runs on a xbox 360 or ps3 can run on this computer.

Furthermore you should worry about the video card for it also always be changed out, and it is quite easy to due (unlike reloading an operating system or changing other computer parts such as the cpu), and it is something you can do quite easily down the road if you want too, beeing easy enough that you yourself can do it TOm and do it under 15 mins once you have the part. The only thing you need to do is know how big your power supply is (it is listed on the side of the power supply so you can always take a picture and take it to a store and ask for help on video card recommendations or just ask people online such as RAFO) and are able to use a screw drive to remove two screws, you simply remove the two screws, unplug a power cable, take out the old card, place the new card in the case, plug in the power cable, and plug back in the two screws. After doing all this you then just install the software cd.

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Good luck Tom, this is something I love doing. I pay for my university by selling computers full time, and I am also a lover of tinkering and changing parts, and my personal computer is my hot rod like to some men their card is their baby.