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.)