This is my first puzzle. That being said, I realize it's not perfect, nor is it forced.

Any way I can slice it, though, ends up with white with a nice advantage.

 Let me know what you think.

A Nice Check. =D

Thanks!  

I'm a total beginner in all this - but surely if black doesn't take the Queen with his pawn (1... gxh5) then white doesn't have the space he needs? If Black moves Queen (1... Qb8), for instance, then he makes room for the King to breathe if White continues to attack. I tried to do a board insert to show what i mean, but couldn't work it! Anyway, am I wrong? (i probably am...!)

You aren't wrong. There are several ways this can go down. That's why I mentioned this wasn't forced. However, if black doesnt' take the queen, he essentially has to move the queen, or else 2. Qh6 Rg7 3. Qh8 Rg8 4. Kd7 Kxd7 5. Bg7!

If he does move his queen, lets say to b8 to threaten the king or c8 to protect his pawn. then it could go

2. Qh6+ Ke8 3.Bxf6 The bishop can't take because it's pinned by the Rook. If he moves Kd8, white can move Bxe7 and he's protected by the bishop. The queen is on the run with a relatively threatening attack. Of course, that doesn't change the fact that this puzzle is not perfect, and for that, I apologize. 

Here are some possibilities.  I'm not sure the queen sacrifice is correct.

ok, thanks. I'm glad i wasn't missing something. to be sure, in a game i'd probably have played black as you suggested up front and quickly lost! easier to analyse after the event...