Also check craigslist but be VERY careful when renting from an individual owner. You MUST do a background check to verify they do not owe more than the property is worth--otherwise you could end up having to show the property to prospective buyers of a Short Sale! Not fun!
If you have a good job and not too bad of credit, you may be able to get a credit union to give you a mortgage if you cannot get a mortgage from a regular lender.
If you have good credit (640 credit score or higher) but haven't been able to save up for your downpayment and closing costs, you may be able to get up to $7,500 from the State of Florida, go here to see if you qualify:
I'm not a lawyer, so this isn't legal advice. For that, you need a lawyer. However . . .
A lease is made between a renter (that's you) and the owner of the property. If the real estate agent and her husband own the property--if they're the property owners--then the lease would be between you and the agent and husband. The question is whether the original owners conveyed ownership via the quit claim deed. It's certainly possible to do so.
It's irrelevant whose name is on the mortgage. That doesn't affect ownership at all.
What the real estate agent/husband did is called a "subject to." They acquired the property subject to the existing mortgage. That's perfectly legitimate and binding. (Well, it's binding, again, if the original owners fully conveyed ownership AND if the quit claim deed was filed with your county. An unfiled quit claim deed is worthless.)
Do whatever makes you comfortable. If that means viewing the deed documents online, fine. If that means going down to the county in person, that's fine.
But the point is that if the quit claim deed was signed by the original owners and properly executed, then the real estate agent and husband own the property. If you want to rent, then you rent from the owners.
Again, I'm not a lawyer, so this isn't legal advice.