Go with the best rate - no matter where it is!!!
Why? Because without a sizeable downpayment you WILL pay MIP and/or MI/PMI REGARDLESS...
Since you are not paying your closing costs anyway, might I suggest an even more savvy approach. If your home is appraised at more than the purchase price, then after you close on the purchase, turn round and rate/term refi your loan. Lenders will not recognize home equity unless it is a refi. Since some of your rate is based on your loan-to-value as is your mortgage insurance rate, refinancing allows you to base those factors on your home's market value, not the purchase price.
Lenders like Flagstar only require one day on title for you to turn around and refi based on the home's appraised value. Anyway, just a thought.