I just covered my old yucky looking cover with a shaped piece if heavy muslin. I can take that off and wash when I like. I use a square of freezer paper on my "most used" spot to keep it looking cleaner longer.
I don't want too much batting on that board. Just one layer of medium batt is enough. You want that board to be quite hard so that your seams press nice and crisp.
I made a small ironing board for taking to classes. About 12 X 18 inches of this board, a layer of batt and a cover of heavy muslin. I use that one a lot, right next to my sewing machine when doing lots of short seams that need to be pressed before they are sewn into something else.
Then I made the 3 X 6 inch one. I was making a table topper and didn't want to put binding on it. So I sewed it RST and turned it right side out through an opening. Then I thought those outside seams would be so much easier to get turned correctly if I could press those seams open first. I made that tiny ironing board, slipped it into the topper through the opening, moved it around as needed to press those seams open, then took it back out through the same hole. Worked fantastically. I'll keep that little ironing board in case I need it again.