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The Cosmology Redshift Survey of the 4-metre Multi-Object Spectroscopic Telescope (4MOST-CRS) will provide redshift measurements of galaxies and quasars over 5800 in the southern hemisphere. As targets for the 4MOST-CRS, we present a selection of an r < 19.25 magnitude-limited sample of Bright Galaxies (BG) and a colour selected sample of Luminous Red Galaxies (LRG) based on DESI Legacy Surveys DR10.1 photometric data, in the redshift ranges 0.1 < z < 0.5 and 0.4 < z < 1, respectively. These samples are selected using the g, r, z, and W1 (from unWISE) photometric bands. For BGs, the star–galaxy separation is performed based on Gaia and Tycho-2 star catalogues. Following 4MOST requirements, the target densities of BGs and LRGs are 250 and 400 , respectively. We quantified the stellar contamination to be <2 − 4% for both galaxy samples using data from the first DESI data release. Using angular clustering, we show that both samples are robust against imaging systematics, confirming a low stellar contamination. Finally, we provide forecasts of the baryonic acoustic oscillation (BAO) and growth of structure (σ8) measurements from the 4MOST-CRS alone and in combination with DESI. From the 4MOST-CRS, we expect 3% and 25% precision on BAO and σ8 measurements, respectively. Combining 4MOST-CRS with DESI improves the constraints from DESI alone by 12% in the 0.4 < z < 0.8 redshift range, leading to the most stringent constraints on BAO measurements from spectroscopic galaxy clustering.