As a buyer, your closing costs will primarily consist of loan costs (i.e. origination fees,points, etc.) plus you'll have a title fee for your loan, and other costs such as recording fees, title company closing fees, and pro-rated amounts for things like taxes, insurance and interest.
Do not confuse closing costs with down payment. Down payment depends on the type of loan you're getting. With an FHA loan, you can put as little as 3.5% down. The more you can put down, the better off you'll be. Anything less than 20% down will require private mortgage insurance (PMI) which is another cost that can either be paid up front (as part of your closing costs) or added to your monthly payment.
I would suggest you start by talking to a lender who can review all of your financial info, and see what you qualify for. They will also give you a "good faith estimate" (GFE) that clearly breaks down all of your costs.
Next step would be to find a good Realtor who can work for you as a Buyer's Agent. Once you find a property you like, you can sometimes negotiate to have the seller pay all or part of your closing costs. Good luck to you!