Graphics for HD video but no gaming

Not much. You should be fine with any 40 dollar GPU.

+ 1 to Littlebro! Your budget and the right mixture of connectors (DVI, HDMI, DP,...) are the selection criteria.

What about this

http://www.newegg.com/Product/Product.aspx?Item=N82E168...

More than enough and has all the outputs you need for different hookups. I ran a 5450 for a few years and it handled HD video no problem and some gaming, so the 6450 should be fine for you.

thats exactly what that cards intended use is but...
if you're motherbd has integrated graphics its also probably enough for HD video.

The Radeon HD 6450 should be ideal if your current CPU is older than an Intel "Sandy Bridge" or "Ivy Bridge" Core i3 / i5 / i7 CPU. It has low power consumption and it also is passively cooled so no need to worry about noise from a fan. Just make sure that your case has good airflow, otherwise it might run a bit hot.