I think there are more questions to be asked before you get a great answer. What price range on the house and the car loan? I'm guessing the biggest point to consider would be your debt to income ratio.
If you buy the car first and take out a loan for it, your buying power will be reduced. When they go to approve you for a mortgage they add up your monthly debts and compare to your income to get the ratio. Say monthly you have a $200 car payment and bring in $2500 and you want to add a house payment of $800. That leaves 32% for the mortgage DTI and 40% for the total DTI. You would also have to add any student loans or credit card payments, etc. You can see that if you instead add a $300 car payment it goes to 32% for mortgage and 44% overall.
One of the benefits to FHA is you don't need a big down payment. Currently you need 3% and in January it will switch to 3.5% down payment. If you can put down a bigger down payment conventional could be a better deal.
