A Simple explanation of the role of video cards in your HTPC

When you play a video on your HTPC the decoding of the video can either be done by the CPU or the GPU (Graphical Processor Unit, ie. Video Card). The advantage of letting the GPU do the decoding is that there is less stress on the CPU which results in lower CPU usage, less power usage and less heat being produced. This is called hardware decoding, which is also known as hardware acceleration / DXVA / CUDA / QuickSync.

All current generation discrete (add on) GPUs and onboard GPUs can hardware decode 1080p, but some current generation GPUs can still struggle with 1080i which requires more work.

What is 1080i vs 1080p

The p stands for progressive video and the i stands for interlaced video. Generally interlaced video requires more work to decode prior to displaying the video on most standard displays. 99.9% of all downloaded videos and blurays/dvds will contain only progressive video. You are only likely to encounter 1080i interlaced video if you are using your HTPC for Live high definition TV via a tuner card.

If you are never going to use your HTPC for live HDTV then you don't need to worry about whether your video card can handle 1080i. If this is the case then the choice of GPU for your HTPC is irrelevant and any option will work fine.

Onboard/Integrated video vs Discrete Video Cards

All computers require a GPU, but this GPU can either be integrated into the CPU/motherboard or it can be an additional piece of hardware in the form of an add-on discrete video card. If using an onboard/integrated GPU then the speed at which the GPU operates also depends on the speed the GPU can access the shared memory (RAM).

Why do people choose to use an Onboard/Integrated GPU?

Can be cheaper
Can use less power
Doesn't take up any room, so can use a smaller case

Why do people choose a discrete (Add-On) GPU

More powerful/faster, therefore better for playing games
Onboard GPU that comes with your Motherboard/CPU might not be fast enough for 1080i
Potentially better quality video output
Easy method of upgrading a current system to cope with 1080P/1080i without having to replace CPU+Motherboard+RAM

Recommendations

Please see below for a list of the 4 different options. If building a new HTPC on a really tight budget I would recommend buying the AMD A6-5400K CPU,+ FM2 socket motherboard + 2x2GB of DDR3-1600 RAM. AMD CPUs are cheaper and have faster integrated graphics than the intel equivalent. Also low end AMD motherboards tend to be slightly cheaper than intel ones.