I imagine they did not have the funds to buy or build heavy military ships, so I wonder what did they use.
Did they re-purpose civilian ships?
I don't think that it is possible to generalise.
I don't doubt that ancient pirates did re-purpose civilian ships in most cases. Indeed, it is said that even sailors on merchant ships which had been attacked by pirates would turn to piracy themselves when they were otherwise out of work. In fact, the number of vessels reportedly used for piracy by the Cilician pirates virtually guarantees that most were re-purposed civilian craft (Strabo writes that Pompey destroyed 1300 pirate vessels of all sizes).
Although not cheap, Philip de Souza's book Piracy in the Graeco-Roman World is well worth reading if you can get hold of a copy. Alternatively, his 1992 PhD thesis on Piracy in the Ancient World is available free online.
Keep in mind that "heavy military ships" were rare -- most galleys were triremes or smaller designs -- biremes, penteconters, liburna. Their construction was well within the capabilities of small ports, and manning them took 50 or so crew -- also within the capabilities of small ports and pirate bands. They only had to be faster than merchant ships, and just about any lightly-loaded galley with a fresh crew could manage that.
And the differences between civilian and military ships were narrow, at times. The Greek penteconter was BOTH.
The pirates used the "same" ships as everyone else. Or at least similar types such as galleys.
In those times, there was (practically) no such thing as "heavy" or dedicated military ships. (OK, a few large ships carried extra (wooden) "armor" or "rams.")
This was before the existence of cannon, or other "missile" weapons for warships that set them apart from other ships. So what distinguished one navy from another was not the quality of ships but the quality of the "sailors," or "marines." (The Roman use of the corvus to pit its superior "marines" against the superior Carthaginian "sailors" demonstrates this principle.)
Pirates, by definition, were better marines and sailors, (except against the professional navy), and that's what accounted for their success. Their ships could sail faster than merchant vessels unless they were also loaded with treasure, and because "incentivized" pirate crewmen rowed faster than crews composed partly of slaves.