Okay, I was now input example of several or many specific pictures of weather places (to element99), & just let me paste in just these visual weather examples first, then continue from that(with that), I think the weather pictures I'll be pasting would look really interesting to look at all together when it's finished creating. Then you can tell me some other things after it.
Apart from a period early in the planet's history when it was raining rocks and comets (which is how water ended up here), most of the weather we get now is what we've always had. Tides were a lot bigger when the Moon was closer to Earth.
Once weather started to become established on Earth there is no reason to think there have been any "types" differing from now; but with varying climate control over geological time due to changes in mean atmospheric and ocean temperatures.
There have been periods of significantly colder warmer times; than ours. These move regional weather patterns around, and modifies their relative frequency and strength, but does not change their "type".
It is important though to correlate signs of a particular past climate in any given country, with where that area of land was at the time thanks to continental drift, collision or rupture.
For example, I live on what is called "The Jurassic Coast" but it is a misnomer because although the rocks extend from early-Jurassic to Cretaceous the coast is geologically recent - the rocks of what is now the SE diagonal half of England were formed on the sea-bed and lagoonal grounds, in sub-tropical latitudes, in an ocean pre-dating the Atlantic Ocean. The world's climate was warmer then than it is now, but the land we now know was in different places.