I can't give you sources explicitly but I can speak to the Romans military effectiveness that so impressed the Greeks.

The first thing you need to understand is how unprofessional the Greeks were, the main reason the Spartans were so scary to the other Greeks is because they were professional.

The second thing to understand is how the romans operated when making war, most ancient army's would not put much thought into how their army's were organized/marched/fed etc. the Romans on the other hand were obsessive. Contrast with the Greeks, who oftentimes only intended on simply showing up to a battle and fighting, with the Romans, who always took great care that their camps were in good defensible positions and had access to water/food. Also everywhere the romans went they built forts. And I don't mean a little ditch and maybe a palisade wall every night like most other army's did (if even that much) I mean straight up Forts. Real hardcore defensible positions that many times in their history saved them from final defeat after they lost a battle in the field and were forced to retreat.

So when you read about Greeks being impressed with the romans, you should read them as a bunch of amateurs used to getting by with the bare minimum of preparation looking at dedicated professionals doing everything that could possibly be done to enhance their chances of winning. Think of it this way: to most people, the battle was what was important. To the Romans, the battle was almost an afterthought, the lead up to the battle was what they spent most of their energy on.

If you want to eat a better picture of this I suggest polybius's (?) rise of the Roman Empire, as he speaks at great length of the organization and dedication of the romans in wartime.