$10,500 is the down payment, and it's the smallest of the numbers you need.
On a $300,000 purchase, plan for closing costs somewhere around 2 to 5 percent, so roughly $6,000 to $15,000, covering lender fees, title, recording, prepaid taxes and insurance. FHA also charges an upfront mortgage insurance premium that's usually added to the loan balance rather than paid in cash, plus an annual premium built into your monthly payment. Lenders will also want to see reserves, meaning money left in the bank after closing. So the honest planning range for that house is closer to $18,000 to $28,000 than $10,500. Get a written loan estimate early, since that's the document that shows the real figures for your file.
On repeating it: FHA generally limits you to one FHA loan at a time, with narrow exceptions. So the 3.5 percent product is usually the first purchase only. People who run this strategy for years tend to switch to low down payment conventional owner-occupant loans for the later ones, which have their own down payment minimums and private mortgage insurance. Ask a lender to lay out the sequence for your situation and confirm current terms in writing, because these programs change.
One cost that catches new landlords: when you move out, your homeowner's policy no longer matches how the property is being used. You switch to a landlord policy, often called a DP-3, and it commonly costs more than the owner-occupied policy did. Call your insurer before the tenant moves in rather than after, because a claim on the wrong policy form is how people find out the hard way.