Bret Devereaux

The next solid 'starting point' book I think is still P. Connolly, Greece and Rome at War (1981), which despite being a bit long in the tooth is an excellent mix of tactics, operations, equipment, individual battles and so on.

More niche topics as you develop that basic knowledge... On the development of the legion, L. Keppie, The Making of the Roman Army (1984) is still a good standard text for the basics of the transitions from the military system of the Middle Republic to that of the early empire.

On equipment, Bishop and Coulston, Roman Military Equipment (2006) is the peerless reference, strongly rooted in the archaeology, for all of your sword, shield and armor needs.

For those with more languages, honorable mentions in the equipment category for Feugère, Les Armes des Romains (1993) and for the reenactor crowd esp., Junkelmann, Die Legionen des Augustus: Der römische Soldat im archäologischen Experiment (1986)

For specific campaign histories of the Punic Wars, J.F Lazenby, The First Punic War: A Military History (1996) and Hannibal's War: A Military History of the Second Punic War (1974) are both very solid, even if I disagree with some of the conclusions re: Carthaginian strategy.

On the late Roman army, I think P. Southern and K.R. Dixon, The Late Roman Army (1996) is still a solid introduction. On that period more generally, D. Potter, The Empire at Bay AD 180-395 (2004) is making some arguments but generally good and very readable.

Also in the very late period J. O'Donnell, Ruin of the Roman Empire: A New History (2009) is a great read and carefully argued even though I disagree quite strongly with its main conclusion. Just a really solid read.

On the costs of fielding armies, @DrMichaelJTayl1 , Soldiers and Silver (2020) was on my blog recommendations and I think is the best thing on the topic with a very solid comparative approach.