I would recommend Polybius as a starting point. Polybius talks a great deal about the Roman army, particularly during the Punic Wars (between 100 and 50 years before, depending on the particular war in question). Polybius is a good source because he was a family friend of the Scipiones (the same Scipiones who produced Scipio Africanus, the one who beat Hannibal) and because he has has descriptions of Roman army tactics and command structure. He writes at length about the levies and how the armies are formed, both infantry and cavalry. Another source is Livy. Livy writes much later (he is a contemporary of Augustus) however he did have access to some good sources. While a decent amount of myth is in his work, information about the premarian army can be gleaned. He talks about early republican tactics, and also talks about the Romans using a phalanx (which to my knowledge has been confirmed by archeological evidence in excavations of the Palatine Hill). Hope this helps!

As others have mentioned, Polybius is your best bet for pre-Marian reforms, specifically 6.19ff. He was a Greek eyewitness to the workings of the Republican army, having been with Scipio at the sack of Carthage. Post-Marian, Caesar's Gallic Wars are useful for the late Republic, and for the early Principate, try Velleius Paterculus.

After the reforms I would suggest De Re Militari by Vegetius for post reform. De Architectura by Vitruvius for a technological view is also good. Vegetius is particularly important for Late roman military structure and remained relevant for centuries after.

Sallust, "Jugurthine War".

Plutarch's Marius biography