Canon 600D has a Canon EF/EF-S lens mount and currently there are 333 native lenses available for this mount.
The latest released lenses that are compatible with the 600D are the Samyang MF 14mm F2.8 Mk2, the Samyang MF 85mm F1.4 Mk2 and the Irix 45mm F1.4.
Canon 600D doesn't have a sensor based image stabilization system but
114 of these lenses already comes with optical image stabilization.
Since Canon 600D has a APS-C sensor, it has a focal length multiplier of 1.6× 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 600D.
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Canon 600D Lenses with Image Stabilization
Canon 600D Lenses with Weather Sealings