For MDF, try a lumber place or home improvement center. They will often cut to size for you.
I have made cake stands with "supplies" from thrift stores. I made one with a 16-inch glass platter ($3.99) plus feet. For feet I used sherbet glasses which I already had in my basement, unused for years, but you can buy those too, or low glass candlesticks, or champagne saucers, or........ whatever your imagination can come up with. Glue the feet to the bottom of the platter with something strong, like epoxy. Another one I made with a silver-plated platter and a silver-plated candle holder. Another one was a special glass Christmas platter and the matching sugar bowl (upside-down) glued together.
All parts were found at the same thrift shop, my favorite.