For what it’s worth I ride a Giant road bike. An OCR1, but now that model goes under the Defy name. Aluminum frame, carbon fork, Shimano 105 components. They have what’s called a compact frame which means the top tube is a tad shorter than a racing bike. This simply makes for a slightly more comfortable position.Specialized and soe other manufacturers make the same compact frame design.
Something like that will run you just over a grand purchased new.
But I agree with JSM, carbon is nice, but very expensive. Aluminum or steel are just fine. A carbon fork though really takes a lot of vibration out of the ride, so that’s a nice plus. But I personally don’t see any difference in frame materials for the average rider. The components are more important. Also see if you want a double or triple crank set. Your Schwinn has a double, and may be just fine for you. A triple helps you get up some hill easier.
So shop for fit, components and price and stick with name brands and you should be fine.
I wouldn’t suggest a Scattante bike though. Unless it has real high end components (at least Shimano 105’s) on it. The low end line of those aren’t that reliable from what some friends have experienced.