What lens can be used with Sony a6000 to shoot landscapes and portraits?

Landscapes and portraits do not use the same lens. There is no lens that is good for both.

Wide-angle lenses are preferred for landscapes, so the current standard lens for mirrorless cameras is 16-50. If you want to take better photos, you can try the 20F28 landscape camera. Large aperture lenses are preferred for portraits, and 50F18 is the affordable option. 35F18 is more suitable for humanities (people + sceneries) rather than specialized portraits. If the price is high, there is 55F18, but the price is around 6K.

The Sony A6000 (also known as α6000) is an APS-C format mirrorless camera, available in three colors: black, white and silver gray. The body is made of plastic material, and the overall design is not much different from that of NEX-6 or NEX-7. There are two mode dials on the body, including internal flash, hot shoe and built-in EVF (electronic viewfinder), including an LCD screen. It is 3 inches, 921,000 pixels.