What size guns did rated and even unrated ships typically use during this time? Imagine the size of the shot would vary greaty between a schooner and ship of the line.
Also, why use a long gun over a carronade or vice versa?
Edit for clarification: I'd prefer the late 17th century to early 18th century, but will honestly take any info I can get.
The "age of sail" could include many centuries. I will just look at sailing warships in the 18th and 19th centuries.
Cannon were rated by the weight of the shot they fired. The most common cannon sizes were 3, 4, 6, 9, 12, 18, 24, 32, 36, and 42 pounder guns.
Ships of the Line would often mount 32 or 36 Pdrs on the lower gun deck and 24 Pdrs on the upper. Frigates would often mount 18 Pdrs. (U.S. Frigates in the War of 1812, such as the USS Constitution, mounted 24 Pdrs, but they were powerful frigates).
Smaller ships would mount smaller cannon. The long 9 Pdr, especially in brass or bronze, (they were more than twice as expensive) rather than iron, was often mounted as bow or stern chasers, as they were deemed to be especially accurate long range guns.
Carronades were short barreled guns, lighter in overall weight than equivalent long guns. As such, they could be mounted on upper decks, and throw a heavy weight of shot (either round shot or grape shot), but they were shorter range and less accurate than long guns. Carronades were first developed in the 1770s.
Ships of the line often mounted 42 Pdr carronades on their upper decks. Heavy frigates sometimes mounted 32 Pdr carronades.
http://www.globalsecurity.org/military/systems/ship/sail-armament.htm
Remember that the Age of Sail is a pretty huge period, stretching from the Spanish Armada to beyond the Wars of the French Revolution. Being that you're asking about carronades, I assume you're interested in the late 18th/early 19th centuries.
Being that you're asking about rated and unrated ships, you'd see a pretty exotic mix. On a first-rate ship of the line, 32-pounder cannon were the workhorse of the ship's armament, though lighter 24-pounders were mounted in upper gundecks to decrease the strain on the ship's deck.
The choice between a "smasher" carronade and a long gun is pretty straight forward. Long guns fired with more accuracy at longer ranges than the short, stubby carronades. Carronandes had huge bores, but could only be used effectively at extremely close ranges.