With 10% down, you are not going to get away from the mortgage insurance factor. Right now, FHA would be your best bet for 90% financing. They do not do risk based pricing for higher loans to value as most othere lenders do, and the MI rates are very reasonalble.
As far as the best deal, rates change daily. So if you get a quote from someone today, and another quote on Monday, the rates could have changed, so the quotes will be moot as far as comparing apples to apples.
Rates also depend on your credit score, income ratios, reserves and other factors. So if a lender does not have 100% of your financial information, they may not be able to quote you properly. Also, just because someone quotes you a rate that involves "no points" doesn't mean you are getting the best deal. Brokers make commission on YSP or yield spread premium, so in effect, you pay a higher rate to pay their commission. This is not necessarily a bad thing, After all, they do deserve to get paid for their work. And getting a loan approved and closed takes many hours of hard work behind the scenes. And they don't get paid unless your loan closes.
In my opinion, your best bet is to talk to no more than 3 brokers or lenders. Pay attention to the fees on the Good Faith Estimates and point blank ask them how much commission they intend to make. Please do not expect a broker or lender to make $500 or so....there is an incredible amount of work involved. An ethical broker or lender won't be afraid to tell you their "fee". No hard and fast rules, but a reasonable commission is in the area of 2% or so of the loan amount. However, it takes just as much work to close a 100K loan as it does to close a 300K loan, so you can see how a broker working a smaller loan may charge a higher percentage. In addition, the broker, like a realtor, does not pocket all of the commission. Usually at least half of it goes to the "house" to cover overhead.
Hope this helps