A two-dimensional model which describes e(g) electrons in a monolayer of an undoped and half doped manganite La(1-x)Sr(1+x)MnO(4) is studied using correlated wavefunctions. The effective Hamiltonian takes into account the kinetic energy, the crystal field splitting between x(2)-y(2) and 3z(2)-r(2) orbitals, and on-site Coulomb interactions for e(g) electrons. They interact with S = 3/2 spins due to t(2g) electrons, which are treated as frozen core spins. Furthermore, the model includes antiferromagnetic superexchange interaction between core spins, and the coupling between e(g) electrons and Jahn-Teller modes. The model reproduces the antiferromagnetic order in the undoped LaSrMnO(4) compound, with occupied 3z(2)-r(2) orbitals and elongated MnO(6) octahedra along the direction perpendicular to the Mn-O plane. In half doped La(0.5)Sr(1.5)MnO(4) manganite one finds robust chequerboard-like charge order using realistic parameters. However, the experimentally observed CE phase is more difficult to stabilize, and we discuss the necessary conditions to obtain it within the present model. Altogether, we conclude that the Jahn-Teller effect plays a crucial role in the entire regime of doping.