Investigation of the non-covalent interaction of biomolecules with aqueous graphene interfaces is a rapidly expanding area. However, reliable exploitation of these interfaces in many applications requires that the links between the sequence and binding of the adsorbed peptide structures be clearly established. Molecular dynamics (MD) simulations can play a key role in elucidating the conformational ensemble of peptides adsorbed at graphene interfaces, helping to elucidate these rules in partnership with experimental characterisation. We apply our recently-developed polarisable force-field for biomolecule-graphene interfaces, GRAPPA, in partnership with advanced simulation approaches, to probe the adsorption behaviour of peptides at aqueous graphene. First we determine the free energy of adsorption of all twenty naturally occurring amino acids (AAs) via metadynamics simulations, providing a benchmark for interpreting peptide-graphene adsorption studies. From these free energies, we find that strong-binding amino acids have flat and/or compact side chain groups, and we relate this behaviour to the interfacial solvent structuring. Second, we apply replica exchange with solute tempering simulations to efficiently and widely sample the conformational ensemble of two experimentally-characterised peptide sequences, P1 and its alanine mutant P1A3, in solution and adsorbed on graphene. For P1 we find a significant minority of the conformational ensemble possesses a helical structure, both in solution and when adsorbed, while P1A3 features mostly extended, random-coil conformations. In solution this helical P1 configuration is stabilised through favourable intra-peptide interactions, while the adsorbed structure is stabilised via interaction of four strongly-binding residues, identified from our metadynamics simulations, with the aqueous graphene interface. Our findings rationalise the performance of the P1 sequence as a known graphene binder.