I was thinking of making some Roman-inspired music so I wanted to know what exact types of percussion their armies used for parades and marches if any at all.
Although I can give you info on instruments used in parades, it doesn't include drums annoyingly. But I'll go on anyway.
I'm going to focus on the pompa triumphalis or triumph procession of the Republic. The triumphant general was given a parade by the senate where they could show off their spoils, their army and themselves. It would wind through the city streets and the citizens would watch from the sidelines. It should be noted that most of the sources, like Appian, Cicero or Plutarch, focus more on the politics and anything controversial rather than stuff like the sounds.
As far as the order they'd process in, first came the senators, leading the procession and symbolically the people. Appian states that trumpeters led the advance of wagons that carried the spoils of war but doesn't say if they precede the senators or not (Pun. 66). Then the spoils come. Behind the plunder come the prisoners. Then comes the victorious general and with him instruments. Appian mentions "a chorus of harpists and pipers" but no drums (Pun. 66). He states that "they march in regular order keeping step with song and dance." Following on from them are the soldiers. Ovid says the soldiers would stamp their feet and chant "Io, io triumphe!" (Tristia 4.2.51-2). Plutarch says the soldiers would sing humorous songs or songs praising the general (Aem. 34). And that's it.
So not much in way of instruments, particularly percussion, but you can imagine the stomping, rhythmic marching, horses' hooves, audience clapping, the trumpets, lyres, flutes and singing making a cacophony. Ovid also says the horses would rise up in confusion and fear from the amount of noise (Tristia 4.2.53-4). Another thing to consider is how with the different parts of procession you'd have one set of noises growing quieter as they moved away and another getting louder as they came closer. And with most of the city made from wood (which, as a side point, the Romans used for resonance in theatres, see Vitruvius, De Arch. V.7.4-7.) or stone, you can imagine it would echo a lot too.