Yes and yes... Modern posters are fine to be rolled in a tube as well as reproductions (if you have any) Older posters, and when I am speaking about older posters I mean from WW2 and prior, I would place acid free paper as a buffer between them and lay them flat. Another member suggested that they store them under a bed which is great if you have the space. It is dark and mostly cool in that environment and that will help maintain the colors of the posters..
I would not suggest shrink wrapping as if I understand the process, heat is introduced to the process and the plastic may not be acid free and could off-gas. IN addition to the off gassing the heat introduced in the process could make the poster paper more brittle in cases where the paper is delicate to start with.. but to each his own..
Obviously in the museum environment I work in we have large metal map case drawers that store many of our larger posters, but we also have some that are so big (outside wall size posters) we have had to fabricate our own storage jackets for them but they work just fine..
Here are some examples of the material from Gaylord. These are archival safe protectors with an acid free stiff cardboard type material and inside is archival safe Mylar that you place the document behind. There is also acid free buffered tissue paper that comes with each folder and can be placed either on top of the picture under the Mylar or on the base of the cardboard for a buffer. Keep in mind these are small size protectors but they come in all sizes, (As big as poster size as well).. The hinge is made of acid free archival safe tape that has no affects and does not come in contact with the paper products..
When I go back to work on Monday, I will take some pictures of the larger size poster holders that we have so you can get an idea of just how big and how many of these products are available through Gaylord and university products..
If I hadn't mentioned before, you have a remarkable collection and your storage capacity and methods are most impressive. Well organized and detailed..