Trying to decide on GPU for a small Home Theater PC

I am going to say you are better off with AMD here.

They have a better lower end and the 7750 uses less power then the comparable NVidia offerings.

One thing of concern is your case only comes with a 200w PSU.

The GT 640 and 7750 will most likely be as good or worse than the HD 4000. For one, they have 1GB 64-bit GDDR5 while the HD 4000 can be set to use 1 GB of DDR3 shared system RAM. I used the HD 4000 for a few months before buying a GPU and I could play almost any game in medium settings in 1080p. Black Ops only ran smooth in 720p. Before you order either of these cards, you should try to set the HD 4000's VRAM to 1 GB in your BIOS if you haven't already done so. It does make a difference. A huge one since the default is 64 MB. Even at 512 MB, the HD 4000 is more than capable of playing any AAA game in low to medium in 720p.

Make no mistake: Intel GPUs still suck.

The HD4000 gets a measly 464 passmark points.
The 7750 gets 1630 and the GT640 gets 1301

This slightly old test shows the intel GPU still being eaten alive.
http://www.techspot.com/review/523-ivy-bridge-intel-core-i7-3770k/page8.html

Notice the parenthesis next to each GPU in those tests, all the other GPUs have the dedicated video RAM size next to the name. The HD 4000, however, shows the clock speed. Since not all motherboards give you the option to change the maximum dedicated VRAM for an HD 4000, then the test is assuming that an Ivy Bridge CPU with the HD 4000 GPU will be running it at its maximum non-overclocked clock speed and stock VRAM size of 64 MB.

I have a i5 3210m laptop and a i7 3770k desktop. I have played several games on both machines. My laptop only has the HD 4000 and I can play any game on it in 1366x768 (which is considered high-def) in medium settings. When I first got the laptop, the BIOS was not updated and there was no VRAM option. GTA IV and Far Cry 3 would not run in any settings or resolution. GTA IV started, but the available VRAM was so low that all you could see is the car and the sky and everything else was black. Far Cry 3 simply wouldn't play. I updated the BIOS, changed the VRAM to the max of 512 MB, updated the HD 4000 drivers from the Intel site and to my surprise, GTA IV not only displayed everything, it was running at a steady 30 FPS in medium settings. I am also able to play Far Cry 3 in 1366x768, medium (default) settings, Directx 9. I have since installed about a half dozen more triple-A games and all play in the default medium settings in 720p or 768.

When I first got my 3770k, I used the HD 4000 to play Black Ops 1, NBA 2K13 and GTA IV. I have a Sabertooth Z77 board which allows me to set the VRAM to 1 GB. NBA 2K13 ran quite well in 1080p but on medium-low settings. Black Ops ran well in medium settings in 720p and GTA IV in 720p and medium.

As for the 640 and 7750, they may dominate in benchmark pi**ing contests, but in real life offer almost no advantages over the HD 4000 besides GDDR5. I also don't see the point in 1 GB on a 64-bit bus when the HD 4000 can have 1 GB on a 128-bit bus if you have dual-channel RAM. Those two cards will give you the same frame rates and limit you just as much as an HD 4000 with maxed out VRAM on its stock clock speed. Even though the benchmark numbers show that they are twice or even almost 3 times as good on certain benchmarks, they are not going to give you twice the FPS. You are definitely not going to be playing BF3 or Far Cry 3 in high-ultra in 1080p with anything close to 60 FPS.

If it were me, the minimum discrete GPU I would get for an Ivy Bridge system with the HD 4000 is either a GTX 650 ti 2GB boost or HD 7850 2 GB. Both will allow you to play most games in 1080p. The only drawbacks is that for an HTPC you are adding more fans. But, at idle or while watching video, these cards are pretty quiet. They are not silent like the 640 and 7750, but they aren't annoyingly loud either. I just feel that any GPU at or under $100 is not worth the upgrade over a HD 4000 as the performance gains will be minimal, none or worse. That, and your PSU is quite small and the HD 4000 adds no additional power consumption on top of the 77w that a typical IB CPU uses.

You could try a slight CPU overclock since you have a Z77 board. Even though it is not a "k" CPU you could raise the clock to a conservative 3.6-3.8 using only the multiplier.

Also, I have not tried it but with the Z77 you can also OC the HD 4000.

Then see if the system is stable and if the game performs better.

+1 for the 7750 http://amzn.to/13IkLk4

BCLK or the base clock will change the clock speed of more than just the CPU. It will affect the RAM and iGPU clocks and might also cause other parts of the system to become unstable; anything that is now controlled directly by the CPU such as the PCI ports, SATA ports and USB. This is why it is recommended to keep BCLK default and simply move the multiplier up and down on newer systems since Sandy Bridge especially on low to moderate overclocks. If you are trying to push your CPU past 5.0 GHz, then it is time to start playing around with BCLK and voltages.

But, in your case since you could benefit from higher a DRAM clock it might be better to just overclock the whole system rather than each individual component. You could still raise the multipliers of the CPU, GPU and DRAM after the BCLK, but make sure you stability test after each incremental increase.

If overclocking doesn't do anything significant, then you will need a dGPU for gaming. Zotac makes a low profile GTX 650 1 GB 128-bit GDDR5. This card is a better comparison to the 7750 as they are both 1 GB 128-bit, are fully powered off the PCI-e slot so require no extra power cable and fall in the same price range. It still has the same mobile GPU core as the 640 but with 128-bit RAM and a slightly higher clock speed. Also, check the detail section of the 640 and 650; the 640 is only DX11 and PCI-e 2.0 compatible while the 650 is DX11.1 and PCI-e 3.0. Being that you have an Ivy Bridge, you will see better performance with 3.0. The extra $20 or so for the 650 is worth it over the 640.

http://www.newegg.com/Product/Product.aspx?Item=N82E16814202002

personally i think an and a10-5800k/a10-6800k is a great option for a HTPC, just find a mini-itx motherboard that is known to support 2133mhz ram with those processors.

the other option is the sapphire low profile 7750 and an intel pentium g2020(or whatever cpu is the best bang for buck.

the intel/7750 option will have a bit more power, about 25% at least, but at the cost of more noise and heat, and will cost about 10-15% more too.

i personally think that a mini-itx case that offers a full size optical slot for an inexpensive($25-35) bluray drive is a must for any modern HTPC.

I think that if you want anything that will play triple-A Steam games in 1080p and in decent quality settings you will have to eventually get an ATX case and a bigger PSU. Other than that, your options are limited to the lower end of the GPU spectrum or just use the HD 4000 since almost every mid-range GPU is now almost 8 inches or longer and of full ATX height. You could always get a horizontal case, they take up about as much space as an A/V receiver or an old VCR but you'd have to make sure the back is open for the fans. Or, you could reverse the fans and have intake blow out the front and the rear exhaust be the intake.

As for PCI-e 3.0 x16, the differences are not that huge compared to 2.0, but your CPU and chipset supports it so you might as well use it. Any boost on a low end card (such as 128-bit VRAM bus and PCIe 3.0) makes a much bigger difference compared to a high end card. You won't really notice the difference between 2.0 motherboard and 3.0 board on a GTX 680 but the 128-bit bus will make a big difference vs a 64-bit.