I know there has been all kinds of incentives lately, and I am not a loan expert, but I had not heard 3% on conventional.
The PMI thing is pretty shitty. Depending on your loan, mine was 180 a month on my first home. Which would be more than an extra payment every year, and meant I couldn't qualify for the quite the home I wanted.
Me being self employed always makes things fucky for financing purposes. I try to make it look like I make as a little as possible for tax purposes, and it fucks me when we are looking for financing.