You might not even want the “ third piece” look for a lot of days, but if you do then I agree that a cardigan, stretch blazer or a bomber that FITS and doesn’t look sloppy are good options.
First I’d decide what bottoms you like & can wear that are durable and washable. Probably pants but trying to avoid baggy sweats. Would you do jeans, chinos or a kind of knit ponte pant with stretch, or a kind of jogger or track pant that’s more fitted or stylish.
I love belting & tucking shirts into my trousers to get a more “ elevated” look, but if I were working with young kids, stooping , sitting on floor or “ little chairs “ I’d do more stretchy waistbands & untucked tops, and want the tops to be longer- ish. So looking for slightly elevated or at least sturdy, not so droopy knits, or I also like button- fronts untucked, but that can be harder to do crisply unless you find the perma- press types.
If you can narrow down some of these preferences & silhouette types, then can see what brands & sources. JJill and Talbots have a lot of coordinated knits but you can also find their lookalikes at lower price points. Athleta has some semi- tailored- activewear hybrids and these looks can also be duplicated or cobbled together from some more discounted sources.