Bakign Stone

I have a stone left over from my MIL's (Mother In Law) house. I also moved into a new house and have a new double oven. The stone its self is about 1.5 inches too long. This is not an issue if I leave it centered some and on the 2nd or 3rd shelf. It fits inside the cavity the window creates. The problem I want to solve is I either want a custom fitting stone (Well 2 so they are easier to store and use) that fits 100% of the flat surface of the shelf. I have seen a couple of people getting items from Home Depot but I am not sure what kind of material to look for. There are a few second hand (Recycled) building product stores in my area. I would like to go armed with the knowledge of what I am looking for. If I can find a stone bigger then my oven I can either rent a whet saw or take it to HD to cut. Can someone suggest what kind of material I can use.

PS I would also like to have the same setup on my outdoor grill.