For most prospective buyers looking to purchase a home, you should plan to have at least a few thousands saved up even if you plan to use the down payment assistance programs. I would say if you can save about $5000, it would be a good cushion (if you end up qualifying for down payment assistance) to prepare you for your home purchase.
As your Realtor, I suggest a great way for buyers to begin to stack up their savings for their future purchase. Prospective buyers should begin a payment shock savings plan. How? Think about the amount of home you would like to purchase. Let me (or a Loan Officer) know so I could provide you with an estimated monthly payment for mortgage on your desired home price. Then I suggest that buyer begin to save the difference between their current monthly rental/housing payment and the amount the future mortgage payment will be.
For example, if buyer is paying $800/mth in rent, but plan to purchase a home that will have mortgage payment of $1200/mth, then each month buyer can put away that $400 difference into a savings account (and DO NOT touch the savings). Payment shock savings gives a buyer good practice, allows them to see if their current budget can afford that mortgage payment and it allows you to save money in the process.