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We introduce a set of four very high resolution cosmological simulations exploring f (R) gravity, with 20483 particles in 768 and |$1536 \, h^{-1} \, {\rm Mpc}$| simulation boxes, for |$|\bar{f}_{R0}| = 10^{-5}$| and Λ cold dark matter (ΛCDM), making the set the largest simulations of f (R) gravity to date. To mimic real observations, the simulations include a continuous 2D- and 3D-light-cone output dedicated to study lensing and clustering statistics. We present a detailed analysis and resolution study for the matter power spectrum in f (R) gravity over a wide range of scales. We also analyse the angular matter power spectrum and lensing convergence on the light-cone. In addition, we investigate the impact of modified gravity on the halo mass function, matter, and halo autocorrelation functions, linear halo bias, and the concentration–mass relation. The impact of f (R) gravity is generally larger on smaller scales and smaller redshift. Comparing our simulations to state-of-the-art hydrodynamical simulations, we confirm a degeneracy between f (R) gravity and baryonic feedback in the matter power spectrum on small scales, but also find that scales around |$k = 1 \, h\, {\rm Mpc}^{-1}$| are promising to distinguish both effects. The lensing convergence power spectrum is increased in f (R) gravity. Numerical fits are in good agreement with our simulations for both standard and modified gravity, but tend to overestimate their relative difference on non-linear scales. The halo bias is lower in f (R) gravity, whereas halo concentrations are increased for unscreened haloes. [ABSTRACT FROM AUTHOR]