Everyone’s budget and definition of frugal is different, but I’ll try to throw out a few thoughts.
I buy specific brands for a few things:
Gap/Gymboree/Lands End for pants because of fit/wear
Carters for pajamas because of fit
new brand names for shoes/boots (Stride Rite, New Balance, etc.) for fit/wear
That being said, I know when the clothing brands I buy are on their best sales of the year and buy what I need then, even if its off season. I also don’t buy shoes every 3 months, I don’t even go in to get them fitted until I think they need new ones. This means we do usually skip a size (or 2). But, I’ve found the brand names shoes do wear better than the cheap stuff.
Through size 5T, I shop a lot at Target. I’ve been very happy with their Circo brand for shirts, shorts (not pants), swimwear, and snow gear. Once they hit kindergarten/size XS its a different story and I go elsewhere.
I don’t shop Craigslist/ebay/etc and I barely shop consignment sales/stores. The exception is Gap chinos which one of mine likes to wear everyday and which are often readily available in excellent condition at consignment sales if I happen to be there.
Finally, I would say think about what you need. And try things on every season to confirm that it really does need to be replaced vs the size on the tag. We do very well on 4-6 outfits per child. It does mean doing laundry more often, but its still the same number of loads. And, they have favorites. Even though I can, and do, use hand-me-downs I prefer to have one child use up the item so the next gets the new/preferred version.