The ideal would be, of course, that the kids get their own clothes in the evening and have them ready to put on in the a.m. I don't have the same floor plan as you, so the bath and the laundry are on the same floor. Usually the kids get their when they get up in the a.m. here, but in your case it would be easier to have the clothes out in the p.m. I'd still supervise the clothes getting; "Ok kids, it's 7 p.m., time to go get your clothes ready for tomorrow." Or something like that.
As to size of the laundry room let me run and measure the area where it will be. (Right now the clothes drawers are in my living room....

) The room is approx. 5' x 10' or 12'. I have a stackable washer/dryer . Each set of 2 drawers is 26" high x 18" wide x 18.5" deep. If you don't have drawers then shelving with bins works well, too. The thing is that you have to weed through the clothes and only keep what is actually
needed and
used, not all the things that are cool, pretty, might be used sometime, etc. Oh, and all church clothes are in my closet. In this way there are always clean, white undershirts for the boys, tights that are clean without holes for the girls, and the dressy dresses aren't worn for a play date in the sand box, etc.