Is that gargling noise coming from the fuel tank? Is this after a hot restart? Can you duplicate the gargling sound by just turning the key to ON without starting the engine? Does this cause an unsteady idle for a few seconds after the startup?
If so, that would be from fuel vaporizing in the fuel return line to the tank and bubbling up through the fuel because the fuel return line check valve (search on those words for info and part numbers) has worn out. This condition is not a driveability problem and should cease when cooler fuel has reached the return line after the engine has started.
The return line check valve is clipped to the tip of the line neaar the fuel pump suction on teh pump and sender assembly in the fuel tank. Unless it is causing a great deal of difficulty, it is not ususally requierd to replace it until the fuel pump needs to be replaced. The same disassembly effort is required for both services.