500GB+ external HDD

So I want to buy a 500GB or more external HDD. It'll be for backup, and to be used to connect to my HDTV to play HD movies, videos etc.

My issue is, that to play Full HD movies via USB in my HDTV, do I need a specific speed/kind of external HDD? Or will any do?
I ask because I had a shitty pen drive which played my full HD videos all choppy. So I just want to be sure before buying.

500GB WESTERN DIGITAL 2.5 PORTABLE Element 500GB - WD External 500GB HDD | eBay
 
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