My kids basically live in the light footed onesies for their first year. I too don't find many in thrift stores, but I can find some decent deals online. I try not to get ones that look too much like pajamas - I prefer the lightweight kind with a zipper on the front, especially if they have tread on the bottom of the feet - or sometimes you can find ones with no feet at all, which is even better when they're mobile. I layer extra shirts on top of that if they need it due to weather. (And if it's warm and sunny, I feel it protects their skin from the sun without being overly warm. But it doesn't get realllly hot here, we're up north.)
If we go out (like to the Y childcare where sometimes I get snide comments about why my babe is in pajamas ) I'll occasionally have them wear two piece outfits, but I don't really like those, as the pants always seem to slide down as they wiggle around, and yeah they press in at the waist - and I really dislike overalls due to how cumbersome some of them are.