Welcome to the ICE section!
First things first. Buying a speaker from Crutchfield is only advisable when a certain speaker is not available here or when there's a big price difference. In your quest for 937s, it's available here with warranty & a very cool price tag. So, I'll rather suggest you to buy here.
2.
It's your front speakers which are more important than the rears. So, it's always worth spending more on the front soundstage.
I'll suggest you to get JBL 607ce Component speaker system for the front to go with the 937.
3.
An amp can make a very good improvement to your car audio. Get a 4channel amp and add to your setup.
4.
In your budget of 10k, it's quiet difficult to get all the above mentioned stuff. So, I'll suggest you to upgrade gradually, ie; step by step.
So, buy the 937 now. After you collect some dough, get Compos and a 4channel amp like JBL CS60.4 and power all the speakers from it.
5.
Since you're considering other brands, I would suggest you to try Hertz. Their speakers sound very good and build quality is one of the best. Their entry level (DIECI series) are far better than other brands which are available on the same price range. In that case, you can opt for a DCX 6X9s for the rear and DSK compos for the front.
6.
Since you're in US now, you can have a look around for more better brands which are hard to get in India. (They may make the pocket a bit lighter though)
7.
Your ears and the thing in between are the best judges for your audio. So, Listen!
Go to a few shops and take some time to check out different speakers. They'll give you a good idea of the way how each sounds.