Get the Nikon 35mm 1.8g DX, its relatively cheap, look for a used one. And then you can get a sony to nikon adapter so you can also use the lens on your a6000 if you want, you won't be able to autofocus with it though on the a6000 without a smart adapter, which is a lot more expensive and frankly not worth the money.
So for your issue about the image not being the same as when you look at it on your pc, theres a few things you can do,
like go to your shooting menu -> set picture control -> and adjust it to your liking, usually people put sharpness all the way up because this is the biggest issue they have, of not being able to clearly tell if subject is in focus. It doesn't change the actual image, but just what is displayed.
You can get an external monitor, or use a smartphone/tablet/laptop as an external monitor to show the live view in a bigger screen so you can see clearly.
But I think the best solution for you would be to tether your camera to your laptop using the USB wire that comes with the camera, so that basically when you take the photo, it'll go directly to your laptop that you'll have beside you and show the actual image there. You can look for the software online, or just torrent Adobe Lightroom.