The inflow of cosmological gas onto haloes, while challenging to directly observe and quantify, plays a fundamental role in the baryon cycle of galaxies. Using the EAGLE suite of hydrodynamical simulations, we present a thorough exploration of the physical properties of gas accreting onto haloes -- namely, its spatial characteristics, density, temperature, and metallicity. Classifying accretion as ``hot or `` cold based on a temperature cut of $10^{5.5}{rm K}$, we find that the covering fraction ($f_{rm cov}$) of cold-mode accreting gas is significantly lower than the hot-mode, with $z=0$ $f_{rm cov}$ values of $approx 50%$ and $approx 80%$ respectively. Active Galactic Nuclei (AGN) feedback in EAGLE reduces inflow $f_{rm cov}$ values by $approx 10%$, with outflows decreasing the solid angle available for accretion flows. Classifying inflow by particle history, we find that gas on first-infall onto a halo is metal-depleted by $approx 2$~dex compared to pre-processed gas, which we find to mimic the circum-galactic medium (CGM) in terms of metal content. We also show that high (low) halo-scale gas accretion rates are associated with metal-poor (rich) CGM in haloes below $10^{12}M_{odot}$, and that variation in halo-scale gas accretion rates may offer a physical explanation for the enhanced scatter in the star-forming main sequence at low ($lesssim10^{9}M_{odot}$) and high ($gtrsim10^{10}M_{odot}$) stellar masses. Our results highlight how gas inflow influences several halo- and galaxy-scale properties, and the need to combine kinematic and chemical data in order to confidently break the degeneracy between accreting and outgoing gas in CGM observations.
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