The Radeon 4350 is the little fry of the Radeon series. The card is not suitable for gaming of any sort, and certainly is not capable of gaming at the resolutions for which most HTPCs will be used. However, an HTPC is not about gaming, is it? It is about playing media - mostly movies and TV shows either from disc or from the internet. Those are tasks at which the EAH4350 is quite good. Reviews have consistently shown that cards based on this GPU are capable of playing back HD content without issue.
Of course, there are many Radeon 4350s. This model, the ASUS EAH4350, is recommended because of its combination of a passive heatsink, 512MB of memory, and a native HDMI port. At $34.99