Bannetons

They're easy to look after.  If you have the true bannetons (lined with linen) the big thing is to knock out excess flour and make sure they can get nice and dry--if they are stored wet with all that flour in there they will mildew.  You will notice that they can get quite damp from the moisture of the dough.  If you store them stacked make sure they are bone dry, but I think you should keep them in the open--they are a nice decorative element to a working kitchen.
If you have the German-style brotforms (coiled willow without linen) they are even easier—you can even leave the flour in them if you want, but it can make a mess when you move them around because you get little chunks of dried flour and water that get everywhere.  But if you clean them out thoroughly, you're just going to end up  putting lots of flour back into them when you use them for proofing.
Bottom line on either--not much point in getting them really clean, since you're just going to saturate them with flour next time around.