Miniature loss with a tactical blow

In a game in which I lost the opening battle as white and ended up with a questionable pawn structure, I overlooked a simple tactical shot and was swept off the board in the matter of a few moves. Here's the game annotated in detail, and the critical position in puzzle form. 

So if you have followed the game with me, we have reached this position:

Black has just played 13...Bd6 with a double attack on h2. It seems white has three plausible candidates: to play 14. Nf3, 14. h3 and 14. g3. Which one would you choose? Give yourself a second to calculate some lines. 

Well, here's how the actual game went: 

Lessons to take away: 

Well, it's clear that I have failed to back up my strategical decisions (to keep playing for a win by holding the knight in the center and the f file open for my rook, passing the ball into my opponent's court to decide between "forcing a perpetual" or playing on) with concrete calculations.

More specifically, when I played g3, I did see that black could force a perpetual with Bxg3 and just cut my analysis there for some reason. It was like feeling you've come to the last stop and you just get off the bus without thinking. Never did it occur to me that black could possibly have more. Lazy me!

And what's more disappointing is the fact that were the position after g3 presented to me as a puzzle from black's perspective, I would have seen the whole thing in a heartbeat. Sigh. But let me end this with a positive: at least, in the moment of a strategical decision, I picked the candidate that I thought was the most aggressive and energetic!

I hope you enjoyed the game and the annotations. Please feel welcome if you'd like to leave any comments. Good chess to all!