Long-period comets reached the Oort cloud (OC) via planetary perturbations and galactic tides. Previous simulations [1] assumed highly eccentric starting orbits. We assume, more realistically, that comets formed with small eccentricities and inclinations. Our goals are to determine (1) the birthplace(s) of OC comets; (2) the highest temperatures to which OC comets have been exposed; (3) whether a massive inner OC exists; and (4) the original mass of solids in the giant planets' region. Using the RMVS3 code, we have integrated the orbits of 900 test particles initially 4-40 AU from the Sun for up to 109 years under the influence of the Sun, the giant planets, and galactic tides. (We plan to model perturbations due to passing stars and molecular clouds in the future.) We find that the fraction of objects that reach the classical outer'' OC is comparable to that in [1], but the number of objects reaching the hypothetical inner OC is smaller. In all of our models, comets originate from a wide range of heliocentric distances. About 80% of the comets first evolve inward before reaching the OC, at which time a typical comet has a perihelion distance near 10 AU. Thus the surface of a typical OC comet was heated to a temperature of order 100 K. Assuming a current outer OC mass of 7M\oplus (1012 comets) and a depletion over the history of the solar system of 40--60% [2], the original mass of the outer OC was 11--18M\oplus. We infer that the original mass of solids in the giant planets' region was of order 100 M\oplus, i.e., only about twice the mass of solids in the giant planets. References: [1] Duncan, M., Quinn T., and Tremaine, S. (1987). {\sl Astron.\ J.} {\bf 94}, 1330--1338. [2] Weissman, P. (1996). In {\sl Completing the Inventory of the Solar System} (T.W. Rettig and J.M. Hahn, Eds.), pp. 265-288.