Animal charcoal is the best substance that can be used in adsorption experiments. This is due to the fact that large surface area available of adsorption.
Porous carbon materials are the best materials for the adsorption experiment (if you want to do some experiment in lab), in case you want to publish the results, you can try the doping of high surface area nanostructures with carbon materials to observe the enhancement in adsorption performance.
The most widely used adsorbent is activated carbon. The Adsorption process is being used by various researchers for the removal of heavy metals from waste streams, and activated carbon has been used as an adsorbent.
Porous materials such as activated carbons, zeolites or even biochar would be good material choices. However, what was found in my group's study below is that Activated carbons performed better at adsorptions of organics.(measured as COD). The coupling with FBR-Fenton processes also introduces adsorption and in-situ regeneration of pores for further adsorption. This FBR-Fenton using GAC as a carrier has shown to have superior degradation performance as well as longevity in its application. Hope this helps cheers.
Article Organics removal and in-situ granule activated carbon regene...
The nature and physico-chemical characteristics of your adsorbate determines determine the kind adsorbent you choose for your adsorption experiment.
But I'll suggest activated charcoal for organic pollutants because of its surface properties as well as its fast adsorption time as noted by several researchers.
For copper (Cu2+ and lead (Pb2+) metals or ions, I'll suggest Clay minerals (Montmorillonite and kaolinite) because of their good ion exchange capacity, surface area& charges and inter-aggregate pores/pore diameter. Surface and inner-sphere complexation reactions are advantages.
Biochar and grapheme could work better for chloride and phosphate and nitrate adsorption.
That would depend on the target of the adsorption process. Carbon-based materials are widely used . This may help: https://www.researchgate.net/publication/337032769_Application_and_prospects_of_carbon_nanostructured_materials_in_water_treatment_A_review
The choice of an adsorbent depends on several factors such as the initial concentration of the adsorbate, the molecular size of the adsorbate, reusability, economics based on operation; just to name a few. Consequently, you would need to carefully consider your experimental conditions before deciding upon a more or less ideal adsorbent.
Several authors in this thread have pointed out pertinent examples such as activated carbon and graphene (both of which have been extensively utilized and studied). A few other noteworthy examples (for your reference purposes) would include aerogels, MOF's, nanofibers, and microspheres.