Using the first-order perturbation theory, we compute the osmotic second and third virial coefficients, the mean-square endto-end distance < R-e(2)>, and the mean-square radius of gyration < R-g(2)> of a polymer near the Theta point. Our model is based on the discrete Gaussian chain model and includes a square-gradient term accounting for the finite-range interaction (characterized by k), in addition to the usual monomer second and third virial coefficients (characterized by v and w, respectively). The use of the discrete model avoids the divergence problems encountered in previous studies using the continuous model. Our study identifies four special temperatures in the Theta regime: the temperature Theta(N) where the osmotic second virial coefficient vanishes, the critical temperature Theta(cr)(N) for phase separation, and two compensation temperatures Theta((e))(N) and Theta((g))(N) at which < R-e(2)> and < R-g(2)> reach their respective ideal values. In the infinite chain-length limit N -> infinity, all of these four temperatures approach Theta(infinity), the Theta temperature for the infinitely long chain. These temperatures differ from each other by terms of order N-1/ 2. In general, these temperatures follow the order Theta(N) > Theta(cr)(N) and Theta(N) > Theta((e))(N) > Theta((g))(N). Furthermore, Theta(N) > Theta(infinity), in agreement with the result obtained by Khokhlov some time ago. On the other hand, depending on the ratio w/kb, Theta(infinity) can be higher than Theta((e))(N) (for w/kb < 9.45), lower than Theta((g))(N) ( for w/kb > 11.63), or in between Theta((e))(N) and Theta((g))(N) (for 9.45 < w/kb < 11.63). Theta(cr)(N) can be either higher or lower than Theta(infinity), depending on whether w/b(6) is larger or smaller than 0.574. From the order of these temperatures, we conclude that the chain is mostly expanded relative to the ideal chain at its Theta(N). However, at Theta(infinity), the chain can be either expanded or contracted, depending on the relative position of Theta(infinity) with respect to Theta((e))(N) and Theta((g)(N) ) and depending on whether the chain dimension is measured by < R-e(2)> or < R-g(2)>.