First off, good call pre-flop, six handed cash game this is a very playable hand some would even consider it a raising hand
Post flop, you should make a bet here. You have a gutshot straight and great flush draw. Dont overbet, just enough to keep everyone interested
The bet was slightly under the pot on the turn, which is ok, maybe even make a pot sized bet. You have to fear an Ace of something, due to the pre-flop raise, so another H hurts if he hold Ah.
You made the right move to raise on the river. Only 1 card in the whole deck loses this hand for you, sure its easy to say you overbet it, particularly as we all know the guys hand.
Personally, even though I dont play NL cash games, I would have made prob a $10/$15 raise. Dont feel downhearted to be in the mindset "how much can I make from this" rather than "Am I actually winning this hand"
I would consider myself unlucky in your position