I've read so many horror stories on this forum about terrible PMs. 

Avoid PMI and then go to a local credit union and get a heloc after closing to gift the money back.Have this as a tool in your tool belt but pursue use of the 3.5% FHA, knowing that you will be at a competitive disadvantage if you are competing with non FHA buyers, then you can call in the favor from your gift person.Just know that if someone gifts you down payment money, your bank will require them to sign a letter stating that it is in fact a gift that doesn’t need to be paid back.

Even more than credit, the more experience and capital you have, the more aggressive a lender is going to be.

Of course credit card is going to be like 3.5% but it does kind of such because it's already hard to get tenants to pay it lol. 

If you're using traditional financing on your primary residence, they're going to do another credit check on you just before closing.

But they were selling an expensive house in California and had horrible credit.

Not for a single airbnb like you are seeking (you and everyone else) but because if you start a BNB or a guest house or a hotel, you can get 40% of your investment back in the form of a tax CREDIT that you can sell for about 90 cents on the dollar. 

Not reported on credit.

Also are you doing credit checks through them?

Use gap funding (credit lines, partners) for the down payment.