Here's what I recently built (HTPC):
AMD Athlon II Regor 240 - $60 or less
780G or 785G motherboard with HDMI ($60 ish)
Decent RAM - probably could do with 2GB, but 4GB will set you back $50-$60.
Optical Drive - $25-30 (more if you want BluRay).
HDD - $50-$100 - depends on size and specs (I went 750GB Green because it was on sale, and will be quiet)
I bought the Antec FusionRemote 350 (includes the 350w PSU)http://www.newegg.com/Product/Product.aspx?Item=N82E16811129046&Tpk=antec%20350
I think I did my build for well under $300 (OS not included). It'll play HD content and pass audio through HDMI. It works perfectly for my needs.
I'd avoid the SSD for booting as advised. For me, that's not a necessary cost.
If you want to go with a more expensive config, check out the tiers on avsforums for help:http://www.avsforum.com/avs-vb/showthread.php?p=14239742#post14239742