I can't see too much discussion coming out of this thread honestly, I mean, you have certain basics concerning all types and then the rest of the thread would be people repeating said notable things. For example, if we're looking at stats you can cover everything very quickly. Electric Types are generally very fast and specially oriented. If we delve into the designs of Electric-Type Pokémon as designs the majority of them are based off of small mammals (Pikachu) or inanimate objects (Magnemite), sometimes being a mixture of both - Dedenne being a small rodent crossed with a pylon in its design is a good example of this. The majority of Electric-Type Gym Leaders are also male, with Elesa being the only female one. There are few secondary Electric-Type Pokémon. Electric-Type attacks are often technical or are moves with additional status effects, such as Ion Deluge or Thunder respectively.
I don't really think there is such a thing as a "stereotype" for a certain type, either. If you want an Ice-Type Pokémon you design a Pokémon who lives in cold conditions (Beartic) or who would be cold naturally (Vanillish). It just makes sense for the Pokémon, and any stereotypes we draw from it would be simple coincedence, honestly. Certain types would be related to either physical or special over the other one because of the kind of type it is. The majority of the elements are more specially oriented (fire, water, grass, electric, poison, psychic, ice) while some elements ARE physical (ground, rock, normal) and then we have some ransom extras (fighting, flying, bug, dragon, ghost, dark, steel, fairy) because why not? Dark would be physically oriented because dark = evil and physical damage is thought of as much more brutal than emotional or PSI damage.
The question shouldn't be "what stereotypes do types have in Pokémon?" but rather "what stereotypes of a certain typing or applied to Pokémon?" For example, Kadabra is infamous for being "based" off of Uri Geller. This is because he uses a stereotype of PSI power - spoons. Even chandeliers are often associated with ghosts and hauntings now (I would assume The Phantom Of The Opera kicked it off), hence Chandelure. Bones are often associated with deserts, which are just sand, which is ground. There you go, Ground-Type Marowak! Wings = Flying so birds = flying type. What is steel renowned for? Being sturdy - almost impossible to break without hydraulics or for some reason a diamond. What does Game Freak do with it? Make it resilient as all hell! Stereotypes from the real world exist in Pokémon, which is why a Pokémon would be assigned a certain typing. Muscular people are generally better at physical fighting, so they are fighting types. If a Pokémon is based off of a bug or arachnid it's a bug type. These aren't stereotypes surrounding Pokémon types these are just facts introduced to a video game. Seriously the basics from Pokémon actually make sense when applied to real-life situations. Fire burns down grass so it's Super-Effective against it. You may not think anything of that now, but when I was a young child and someone would ask me a question like "how do you put out fire?" I could say "pour water over it or snuff it out with rocks or earth!" This is because this types are Super-Effective against Fire in Pokémon. As such, many Fire-Type Pokémon are portrayed as being susceptible to water. Take Torkoal for an example - it has holes in it's impenetrable shell; water or earth could pass through there easily. This is even highlighted with Charmander's Pokédex where it says putting out the light on its tail will kill it.
As such, the question of "what are links in typings of Pokémon" would be answered quickly and would be a fairly boring point of discussion. If you try to look for more links you will be surprised at how well thought through the typings in Pokémon are. Trivial things like water putting out fire really makes sense for the much younger age group, and the designs complement this well. Pokémon has that certain level of complexity with its typings and its Pokémon. Take for example Mawile. A 6 year old would think "it's Steel because it's grey and is made of iron, and it's fairy because it wears a little kimono! :D" whereas if you look further into it it's based off of the Yoko-onno (<-- that's from memory, I probably got the name of it wrong, or I'm thinking of entirely the wrong thing lol) and its typing makes even more sense.
Like I've said before, associating stats to types is trivial, because the typing only has that stereotype because of the Pokémon in the group, who are, for the vast majority of the time, anyway, oriented in that certain manner because of other reasons. Fire is an element, it would logically be more specially based. Fist-fighting is very physical, so the Fighting type would logically be a physically oriented typing (but they have to train their bodies and minds, so they have good Special Defense). Seriously you can throw any honest stereotype of a typing at me and I can find a reason for why it would be that way, because everything in Pokémon makes sense. This is why I consider it to be the greatest franchise of all time. It has so many appealing factors to all age groups, nationalities etc.. It is so diverse a person with a certain interest or hobby will likely find a Pokémon based off of said interest and it can become their favourite. They can participate in talking about Pokémon thanks to the different media, too. If they're not very good at the battling said, they can just watch the anime. If they think they're ready, they can try reading the manga, even though it would probably ruin a 5-year old's mind. However the manga then appeals to a college or university student!
And, like normal when I make a long post, I got sidetracked. Point still stands, I urge people to look further into WHY a certain type has its stereo-type, instead of just saying "Electric-Types are fast! :)"
tl;dr: Pokémon makes sense; it appeals to all age groups; look into Pokémon more and you will probably learn something; more stuff I forgot that I typed up.