There are several choices available to you if you have a small down payment saved, or if you don’t want to use up all of your savings on a down payment.
FHA is always a good low down payment option at 3.5% of the purchase price and, paired with any seller or lender credits to cover closing costs, can get you from renter to homeowner with a very modest investment.
Fannie Mae offers their Home Ready loan program.
Freddie Mac offers their Home Possible program.
And of course there are several CalHFA Down Payment Assistance programs, (restricted to First Time Home Buyers) both loans and grants, that can help you buy a home with very little money out of pocket.