I am by no means a historian, I just happen to have a passing interest in naval history. The earliest turreted warship I can recall is the early ironclad USS Monitor that famously dueled her confederate counterpart Merrimack during the American Civil War at the Battle of Hampton Roads.

The transition from wooden hulled ships to steel occurred with the improvements in steam propulsion systems, and later the use of coal and oil-fired boilers. With the massive improvement in horsepower these afford you, ships can afford to be much more heavily armored. The invention of turrets came from a switch of focus on having many cannons as with the ships-of-the-line from the age of sail to having fewer guns with far greater range and striking power to defeat the new heavily armored ironclad ships. These large guns are very heavy, and it's uneconomical to place them around the whole outside of your ship to be able to shoot in all directions. Thus, turrets.

My question is when did ships start using turrets for guns instead of the massive broadsides common with wooden sailing ships.

Broadsides started getting smaller once people built ironclads (well other than the french ships Magenta and Solférino). Turrets first appeared in 1861 but their weight and that they got in the way of the sail limited their popularity.

Was there any in between ships?

Central battery ships. And just about everything built between about 1870 and 1890.

It seems to me that there is some discussion of the ironclads used in the US Civil war, but not a great deal of information between that time frame and say WWI when the use of steel built warships with turrets was common.

There is quite a lot of information although it doesn't get much profile due the limited amount of action such ships saw. Useful terms are ironclad, Central battery ships, steam ram and William Frederick Mitchell.