The House of Miniatures™ kits are really excellent. They are very consistently cut to the right dimensions and the grain is very uniform. Even the routing work is very good.
Ultimately, a perfect period finish comes down to a smooth, glassy look and even shading on all parts of the piece of furniture. Choices of materials and the technique you use are important as well. But the patience and skill to prep the surface, both initially and between coats, is worth learning. The enjoyment of a job well done is lasting.
Each kit has a parts layout sheet in the instructions, usually before the assembly instructions begin. It is placed in that location with good reason: so that you will check your parts before you begin your build.