It's good that you've been saving money because lenders want to see a pattern of savings and some cash reserves on hand in addition to the money you'll need for a down payment and closing costs. An FHA loan can be a good option for you for two reasons:
A down payment of 3.5 percent on a $250,000 home is $8,750, so you'll need to save more fast if you want to buy soon. Don't forget you'll need an extra cushion of money for emergencies, closing costs and moving expenses. If you can't save enough, you should explore other options for down payment money. Can you take on a second job or overtime at your current job? Do you have anything you can sell to generate some extra cash?
If your parents or other relatives can help you, they would need to sign a gift letter telling your lender that you don't need to repay the money.
Other options include looking into down payment assistance programs from your state or local government or even your employer. You can usually find them through your state housing commission. Some of these programs are restricted to first-time buyers or by your income level. Most good lenders know about these programs and can help you find some extra down payment money.