I think that the APR for most VA military loans is going to be pretty consistent accross the board (within 0.25% at least), so your best bet is to look at what "additional" fees you'll have to pay. I'd go with the lowest APR (in the 0.25% window), and with the institution that is going to charge you the least amount of addtional fees. From personal experience, I've seen: loan origination fees, credit check fees, processing fees, EFT fees, appraisal fees, title agency fees, and don't forget the Goat's "I-just-got-some-coffee-so-pay-us" fee (here). Not all of these fees are standard, but you should be able to ask your lending agency a list of all fees they may charge you before you sign on the dotted line. This way you'll know more about what you're getting into and be able to make an educated decision! Hope this helps you make a smart decision on your military loan.
My opinion on VA military loans