So much depends on individual school’s dress code. What is fine at Masters/George with 7D2 would not have been within dress code for St. Andrew’s for 7D1.
For dress code schools that require things like khakis and a blazer/shirt & tie for boys (and similar level of “nice dinner with grandma” clothes), here is where I would go:
The OUTLET version of any brand like J. Crew, LL Bean, Gap, Ralph Lauren, Banana Republic, Brooks Brothers
Also the regular store/website of the above brands.
Lands End used to have a hipper line called Canvas, but a quick search seems to indicate that they folded that
LL Bean Signature is a little more hip than the regular stuff, but often pricier
Target — not bad for staples like shirts
Uniqlo — their stuff is generally a very good price point, and sometimes more interesting than brands above (for example, the line Ines De La Fressange did/does for them)
One thing I want to recognize is that everyone has a budget and everyone has a frame of reference. So recommending something like Cole Haan (or J. Crew) to someone who does not have that as a frame of reference, $100 (and up) on a pair of ballet flats or $175 on a blazer is going to seem ridiculous/wasteful/bougie/unaffordable.
My advice for kids looking to “fit in” and parents looking to equip them is to know your budget, and stick to your budget, as well as your family’s sensibilities. As long as you are in dress code and the stuff is relatively durable, you’re good. I don’t want any new BS family to think they have to buy this item or that item or junior will look like an outcast.
That said, it’s not a bad idea to get a few hardwearing classics. Bean Boots (keep your feet dry, too!), a J. Crew/Brooks Brothers blazer, Barbour jacket, etc.