You are absolutely correct about velvet (generally the die is the problem here) and oak (the tannic acid is the problem here). But there are several other things to avoid. At all cost avoid all particle board and any product that is made with Urea-formaldehyde or any urea based glue. This includes plywood and some versions of MDO products. I am unfamiliar with the foam you mention, but I would be very, very reluctant to use any "foam" product. Even if it doesn't come in contact with the object, there the problems with off gasing are tremendous in most cases. With regard to direct contact with the objects, most sources recommend plain white acid-free cotton muslin. It's not very attractive, but it won't damage the objects. The Institute for Museum Services is a government agency and its forerunner used to issue booklets for small museums to use as guidelines in various products. You might try looking there. The American Assoc. for State and Local History also put out booklets about designing displays. See https://www.aaslhnet.org/aaslhssa/ec....shopping_page
There are also several good books on the subject, but I can't seem to find any titles right now. Another source of material is the company Light Impressions out of Rochester, NY. Then started with archival stuff for preserving paper and photos, but many of their products would be helpful to someone building exhibit cases.
One of your primary concerns should be the finish that you put on the wood, if you decide to use wood. Most of the companies out there have webpages that offer details about their products, off-gasing, etc. Be very, very careful about the finish you use and consider putting some sort of acid free barrier product between the finish and the objects you choose to display.
Finally, there is the surface through which you will be viewing these objects. Make certain that it is UV filtered. Also make certain that you include some sort of temperature and moisture metering device so you can tell at a glance if there is a problem. You don't need to spend a fortune here, just the little stip meters will do fine. Best of luck and keep us posted. We want to see photos when it's all done. Steve