When I was growing up we had the 'built-in' ironing board that folded into a niche in the wall. It was wooden with a canvas cover, to which my mom added a piece of an old mattress pad and then covered with a piece of an old sheet.
It was much more stable than any of the free standing ones I've had since.
I now have one of the small 'over the door' ones that is also quite stable, but not really big enough.