Currently there are 20 native Standard Zoom lenses for Sony A77 and all of these lenses are autofocus (AF) type.
A77 also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on A77.
Since Sony A77 has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 3 Standard Zoom lenses with Weather Sealings.