What are the specifications of the paper required for pencil color drawings?
There are several characteristic for a paper that should influence your choice :

The weight

The higher this value will be the thicker and the studier the paper will be. It is usefull to have a rather high value, because you will be able to erase or burnishing, without completely destroying your paper. Personnaly I thing that having 200 gsm is enough, but maybe if you erase a lot and have hard pencils it would be a good idea to aim higher.

The tooth

It designs the microscopic grains on the paper that hold the pigments. Thus a paper with more tooth, will be able to receive more layers. But it is possible to apply several layers on paper with less tooth, but your first will have to be very light, otherwise the paper will saturate fast. On the other hand if the paper is very rough, you will have a different finish than on a smooth surface.
For watercolor papers it depends of the denomiantion from the smoother to the rougher, you have : Hot press, Cold Press, Rough.



Acide free paper

If you want a paper that last longer (less yellowing for example) you can use an acid free paper, but since you use student grade colored pencils, it not really necessary.

Products

You can try some hot press watercolor paper, and maybe cold press if you feel like you can't layer as much as you wish. If you have some smooth bristol at home, you can also try to work on this paper. Personnaly my favorite paper is the Stonhenge drawing paper, but it may be expensive. You can also use Canson Mi-Teintes if you want to draw on a colored surface, but becareful one side is too rough.

You can find here a comparison of different papers, but the colored pencil used are artist grade. It can give you an idea of the finish of your drawing depending on the paper you chose. Comparison of papers