(Consider this answer a draft till I do aome more searching)

You mentioned a few option that might work, that is centrifuge, sand bed or coal filter.

I suggeste taking a largish sample of your water and doing bench scale tests with each sand bed and coal filters.
I also would try to let the material settle - just leave a batch undisturbed in a clear container for a few days or weeks, and see if the material settles. If it does, a centrifuge might work - or you simply build a settling tank.
But I think you need to start with experiments, those will tell you mroe than the internet ever can.

(Consider this answer a draft till I do aome more searching)

Regarding Distillation, the most efficient sea-water distillation plants need 23-27 kWh/m³, a small scale batch system will probably be far worse. Distillation plants are also pretty expensive.

You mentioned a few option that might work, that is centrifuge, sand bed or coal filter.

I suggeste taking a largish sample of your water and doing bench scale tests with each sand bed and coal filters.
I also would try to let the material settle - just leave a batch undisturbed in a clear container for a few days or weeks, and see if the material settles. If it does, a centrifuge might work - or you simply build a settling tank.
But I think you need to start with experiments, those will tell you more than the internet ever can.