Specifically, I'd like to know about British, Spanish, French, and Dutch warships and what their colours looked liked.
Would colours look different depending on the part of the ship? (broadsides, stern, bulwarks, bow, deck, etc.)
What classes of ships were there? I am aware of the following classes that existed in history ; cutter, schooner, brig/brigatine/frigate/heavy frigate/man o' war/ ship of the line. What would these ships look like, in terms of shape and sails? Were there other classes of ships, too?
I would also like to know how many cannons from each ship class would be carried on each ship (not only just the broadsides, but the bow and stern, too)
I would also like to know if the different nations I mentioned had different names for ship classes (e.g. one nation refers to them as Cutters, but the other empire refers to them as Gunboats)
This is a gigantic question that I'm ill-prepared to answer with regard to any nation other than Britain.
In the case of Britain, I cannot recommend enough trying to get your hands on a copy of Cdr. Charles N. Robinson's The British Fleet, originally published in 1895. Your best bet is through ILL.
To answer your question with regard to the Royal Navy, there are two issues. The first is the paint, and the second the armaments and design. The second is easiest to answer, as the rules classifying ships as first-rate, second-rate, third-rate, fourth-rate, and fifth-rate were laid out in the 1706 Establishment. This was a formal building program initiated by the Navy Board in that year, and which stood for a couple of decades before being revised.
The first question, regarding paint, is more complex because that was generally up to the captains who commanded His Majesty's ships. The Navy provided yellow paint, necessary to help keep rot and insects out of the timber, but captains needed to dip into their own pockets for anything fancy. That being said, as far as I'm aware nobody was sailing around on a 100-gun ship of the line painted like a bag of Skittles. Yellow, with black, white, or red highlights seemed popular, based on contemporary paintings.
Building model ships has been a popular hobby for a long time, so if you try to look up a particular vessel's paint scheme, it's likely that you can get a decent idea of how she looked. In fact, a book intended for hobbyists, British Warships in the Age of Sail 1603-1714, by Rif Winfield, is just the sort of encyclopedic text that should serve you fairly well.