Manga has a very very large variety of genres, just like most comics.
However, when it comes to mainstream manga, they tend to be targeted at teenagers. The two major genres are shonen and shojo.
Shonen manga tend to have a teenage male protagonist who tries to be the very best at something. Best at sports, best at fighting, best at card playing, best at being a ninja, etc.
There are also ones about a teenager interacting with a ghost or demon, that is very common.
Shojo manga tend to have a teenage female protagonist and tend to focus more on romance. They usually take place in school and the main lead tends to be awkward and clumsy.
Another type of manga you might come across are Moe mangas. They tend to take place in high school and have multiple female leads and sometime little to no male characters. The characters tend to be "super cute" and have huge eyes.
Pokemon falls into kid manga, which tend to be about friendship and collecting things and competing in tournaments. But there are also kid manga about kids just doing kid stuff and they might have a robot or animal sidekick.