What 3D CAD and CAM options work well on Linux?

FreeCAD is a sensible place to start if you want a native desktop option. It includes a CAM workbench, so you can model parts and explore toolpath generation in the same application. Check whether its current workflow and post-processors support your machine before committing to it.

For the CAD side, BricsCAD is another option that runs on Linux, but it is commercial software. Whether it suits you depends on the kind of modeling you need and your budget.

Keep the machine control and CAM steps separate in your search. LinuxCNC is for controlling compatible CNC machines, not a replacement for CAD or a toolpath-generation package. You still need CAM software that can produce suitable output for your controller.

There are also browser-based CAD services with CAM features. They can work from Linux without a native Linux application, but they rely on an internet connection and cloud-based workflows, so check the feature set and access terms before building your process around one.