In our home a cleaning caddy works really well. We have previously put our window washing tools in a basket and had a neat pile of cleaning cloths on the shelf. But this is nice, we can keep some of the child's essential cleaning items together, it's completely transportable and really easy to use.
We have a dusting brush, cleaning cloths (blue), cleaning mitt (yellow), a small spray bottle and our window washing set (all of these materials are from our little shop however our cleaning cloths and cleaning mitts are sourced from Handmade Montessori). A scrubbing brush, sponge or towel could be useful also.
Kept on the shelf for when the need arises.
A couple more cleaning caddy pics here.
P.S. Also have a look at this kid's cleaning bucket at Making Montessori Ours.