Understanding the uptake of nanoparticles (NPs) by different types of cellular membranes plays a pivotal role in the design of NPs for medical applications and in avoiding adverse effects that result in nanotoxicity. Yet, the role of key design parameters, such as the bare NP material, NP size and surface reactivity, and the nature of NP coatings, in membrane remodelling and uptake mechanisms is still very poorly understood, particularly towards the lower range of NP dimensions that are beyond the experimental imaging resolution. The same can be said about the role of a particular membrane composition. Here, we systematically employ biased and unbiased molecular dynamics simulations to calculate the binding energy for three bare materials (Ag/SiO2/TiO2) and three NP sizes (1/3/5 nm diameter) with a representative lung surfactant membrane, and to study their binding kinetics. The calculated binding energies show that irrespective of size, Ag nanoparticles bind very strongly to the bilayer, while the NPs made of SiO2 or TiO2 experience very low to no binding. The unbiased simulations provide insight into how the NPs and membrane affect each other in terms of the solvent-accessible surface area (SASA) of the NPs and the defect types and fluidity of the membrane. Using these systematic fine-grained results in coarsening procedures will pave the way for simulations considering NP sizes that are well beyond the membrane thickness, i.e. closer to experimental dimensions, for which different binding characteristics and more significant membrane remodelling are expected.