The Trade Federation has a fleet sufficient to blockade Naboo.
Its large military fleet therefore includes at a minimum the "hundreds" of battleships stated to be blockading Naboo, and quite possibly thousands of capital ships overall.
Although the battleships of the Trade Federation are quite large, their quality is questionable. Their utility in battle appears limited by too great a reliance on automation and centralization.
It appears likely that most of the ships in that fleet were originally intended for shipping - hence the large hull volumes and light armament - but the sheer quantity of cubage remains impressive, as do the sheer numbers of droids that can be packed into that cubage.
At this point in time, the Republic does not appear to operate warships, although it is not unusual for private ships to be armed, or for planets to have some military ships on hand (e.g., Naboo has a number of starfighters.)