Is there a field guide to ECC for the IT Security layman?
By non-standard do you mean when to use custom curves? Like in crypto++ where you can specify your own parameters? 

Given that the standards recommend certain sets of domain parameters (and interesting enough US government departments are forbidden from using their own parameters) it's sounds like the answer is no, for reasons of avoiding the risks of self implementation and the worthlessness of "security by obscurity". Tiresome, but this is how i answer all the "should I do my own" question, sorry.

I do know that NIST curves have certain computational advantages over any old curves because there are some just more convenient numbers for the Projective coordinates calculations. Also this wikipedia page seems to think the number of prime curves and binary curves affects security and implimentation efficiency (I have no idea why though, but there is a link in the "NIST-recommended elliptic curves" section )