Studying from first principles the competition between ferromagnetic (FM) and antiferromagnetic (AF) interactions in the charge-transfer-insulator GeCuO3, we predict that a small external pressure should switch the uniform AF ground state to FM, and estimate (using exchange parameters computed as a function of strain) the competing AF couplings and the transition temperature to the dimerized spin-Peierls state. Although idealized as a one-dimensional Heisenberg antiferromagnet, GeCuO3 is found to be influenced by nonideal geometry and side groups.