I do not think you will avoid PMI if you cannot drop the 20% down...though with good credit scores like yours that would be a conversation to have with your lender of choice- the bite they take for PMI MIGHT not be as big. I have several lenders to recommend if you want recommendations.
The reason NH Finance and FHA is good these days is that they let you borrow up to 97% as I understand it, which approaches the old days of piggyback loans on a first at 80% and a second home equity loan at 20% BOTH signed at closing. Yoiu still have to cough up 3%. Again, I am not the financial man, I am not a lender, but I am pretty sure I have this straight. Also, the FHA guidelines have been severely loosened so the property does not have to pass muster on as many fronts as it used to.
My point is as you STILL therefore have the ability to borrow a lot with an FHA loan and hold onto your cash since you are financing a good proportion of your purchase, it is in my opinion a good time to buy, let the appreciation ride up over the next 5-10 years and either sell then or when more toward the a new market top, or if you intend to live in the house you will have at least had a chance to let your $40,000 build up over time provided you have made some safe investment decisions in a well diversified portfolio. The gap in home prices typically fills in quickly once there is recognition that the bottom has been reached. That recognition appears to be happening now at its beginning stages. You will have something of value IF YOU CHOOSE THE RIGHT PROPERTY, let it appreciate, then either sell it or pay down you mortgage with a lump sum payment (make sure there is no penalty for prepayment on your loan). The interest rates you catch now will likely be lower than if you wait to buy. My advice is to stay with a fixed loan. As oil becomes more expensive, companies will be forced to raise costs which will in turn mean that inflation will present as an issue and that borrowing money will become a riskier proposition and interest rates will go up. Again, check all this with you financial advisor or talk it through with a lender.