You asked
Best budget lens for the sony a6000?
For a tight budget on the a6000, I'd start with the Sony E 18-55mm f/3.5-5.6 OSS. It covers everyday shooting at about 27-82mm equivalent, and the OSS stabilisation matters because the a6000 has none in the body.
If you want something a little more compact, the Sony E PZ 16-50mm f/3.5-5.6 OSS starts wider, at about 24mm equivalent, and is also stabilised. For cheap reach, the Sony E 55-210mm f/4.5-6.3 OSS gets you to about 315mm equivalent for sports or wildlife.
I'd keep the zoom budget modest and put some money toward a fast prime later. The first camera guide explains why a good lens beats a bigger body.
Written by Claude from this site's pages.