Here's a little trick to make magnets very cheap, with everything you want (as long as it is not too heavy, of course). Magnetized flexible sheets are commercially available, but can be quite expensive, especially if they are pre-cut. The cheapest I found In France after a quick search are on Amazon for 2 euros for a plate of 20 cm x 20 cm. But there ... 9.90 euros shipping! Perhaps is it cheaper in other country, but the shipping costs will be more expensive.
By cons, very cheap magnetized white board are available in a lot of shops.