My rule of thumb for the kids has always been:
2 full weeks of clothes per season from the skin out. Including underwear, undershirts (if needed for your climate) and socks.
1 full week of clothes for "in between weather". We have a lot of that around here here in the spring and fall.
1 full week of pajamas per season.
1 dressy outfit per season/or if you attend church, no more than 4 dressy outfits with shoes, socks and/or tights per season.
1 winter coat, 1 light weight jacket, 1 sweater or sweatshirt.
1-2 pairs of shoes per season, includes athletic shoes for school and sandles for summer.
Also you may want to include for your climate, snow pants, rain coat, boots and gloves.
This is a bit more than "need", but it will allow you to go for more than a week if you can't wash clothes.
Put away the clothes out of season in plastic boxes.