Knowing which Polk speakers he currently has would be helpful. He wants a 5.1 setup? Budget is low for a decent 5.1 outside of an HTIB like the folk are BB are pushing (I'd not go with Samsung personally at all except maybe for a tv). He has a tv with hdmi capabilities, is he using OTA reception or sat or cable?
He should look at multi-ch avrs, not stereo receivers. He may not need all the bells and whistles but they have superior features to those stereo units and economies of scale. Budget avrs at accessories4less.com can be had. At the least for the bass management for the sub, an avr is way better than the stereo receivers that don't have any. He can always use the 2 speakers with a sub (2.1) and build up from there, but 3.1 probably a better start.
Any chance on a bit better budget? Help out the old man if you've sunk thousands into headphones!
The Yamaha 8" sub isn't much of a sub to me, I'd rather have something from Dayton at the low end of the price range (parts-express.com is a good place to start).
PS comparing these fake added up "watt numbers" for the receiver is meaningless, let alone the wattage ratings for speakers. Total sales garbage on the receivers and often not much more meaningful for speakers without consideration of specs that mean more. Look at the actual specs, not what the marketing/sales folk did....