1. Armored cruisers have a belt of armor protection and carry guns up to 10 " in size. These ships steadily grew in size during the brief ten year period they were being built. The ten armored cruisers built by the US Navy were so large, they were originally given state names and treated like a capital ship.
2. Sir Jackie Fisher of the Royal Navy designed Battle Cruisers specifically to deal with armored cruisers. His battle cruisers carried battleship size 12 ' guns or bigger. They had steam turbine power plants and were faster than the armored cruisers built between 1894 and 1906. Battle cruisers initially had armor plate that was on the scale of an armored cruiser, but later ones had somewhat thicker armor.
3. First class cruiser. I do not know enough about that term to comment on it.
4. Heavy Cruiser. In 1922, the leading navies of the world signed a treaty that limited naval armaments. Cruisers were limited to 10,000 tons and guns were limited to 8 ". Some of the older, pre world war I armored cruisers were renamed heavy cruisers, but nearly all of these old armored cruisers were scrapped by 1930.
5. Light Cruisers were post Washington Navy treaty protected and scout cruisers. They carried guns of 6" and were often considerably smaller than the 10,000 ton limit. Exceptions to that rule were the Japanese Mogami class, the Royal Navy Southampton class and the US Navy Brooklyn class light cruisers that were close to, or over the 10,000 ton limit and carried 12 or 15 six inch guns.
6. Protected cruisers had an armor plated main deck, but did not have an armored belt.
7. Scout cruisers carried no armor at all. They were roughly the size of a protected cruiser.
   Before 1914, armored cruisers were considered to be heavy cruisers while the protected and scout cruisers were considered to be light cruisers. Most light cruisers were in the 5,000 to 8,000 ton range of displacement and most armored cruisers were above 8,000 tons in displacement.
   During World War II, a new cruiser type was introduced. The Anti-Aircraft cruiser. These ships were light cruisers that carried high angled anti-aircraft guns. Examples are the Royal Navy Dido class and the US Navy Atlanta class.
   Source: Jane's Fighting Ships
   "Warships of World War II" by Anthony Preston.

Armored Cruisers and Protected Cruisers are often conflated together but they are in fact operating on very different principles.

The armored cruiser was the initial stepup from an ironclad. The idea was that the ship would wield a "belt" of armor around its side, protecting the sides from gunfire. While effective at mitigating damage, the problem was that the belt of armor was very heavy, making the cruiser slower. As a speedier option, protected cruisers shielded the ship only below the waterline and the decks, thus, "protecting" the important parts of the ship like the engines and ammunition storage. They had less armor and thus were able to be speedier than the armored cruisers, but at the cost of having more vulnerable sides.

First-class is just a term to denote the largest and heaviest ships of a certain class. For instance, the US denoted ships with 40-or-more guns as being "first class" while ships with 20-to-40 were "second-class."

At this point, armored cruiser development split two ways: the first was for a heavier cruiser that would be capable of taking out other armored cruisers, while being faster and less armored than a battleship. This was the battlecruiser, which over time became more and more like a full battleship (although some examples were considered "fast battleships" like Graf Spee and arguably the Japanese Kongou class).

The other evolution path was simply to make tougher light cruisers which would be relatively easy to produce compared to a battlecruiser or battleship, but would still be able to fight enemy light cruisers. These larger light cruisers would eventually become designated as heavy cruisers, and would supplant the role of the "regular" armored cruiser (as the designation for heavy cruisers, CA, originally referred to armored cruisers).

Lastly, scout cruisers were essentially "light" light cruisers, used primarily for reconnaissance and leading destroyer squadrons. Their role was eventually supplanted by light cruisers.

You also had auxiliary cruisers, which were essentially merchant ships armed for combat (they usually played a merchant raider role, like the auxiliary cruiser Thor), and anti-aircraft cruisers (like the Atlanta-class CLAA) which were cruisers equipped with less cannons and more anti-aircraft weapons, used in an anti-aircraft screening role. These eventually evolved into the guided-missile cruisers that we use today, which retain their air-defense role, for instance with the AEGIS system as on USS Ticonderoga.