Sony A6300 has a Sony E lens mount and currently there are 116 native lenses available for this mount.
Sony A6300 doesn't have a sensor based image stabilization system but 30 of these lenses already comes with optical image stabilization.
Since Sony A6300 has a APS-C sensor, it has a focal length multiplier of 1.5x so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on A6300.
You may also also be interested in these:
Sony A6300 Lenses with Image Stabilization
Sony A6300 Lenses with Weather Sealings