It depends on what genres you like. There are many different kinds of genres and manga covers a lot if not all genres. You should also look up a deeper definition of what shojo and shonen means because I will be using those terms. Shonen essentially means it's aim for guys, Shojo is aimed for girls. So here are some few suggestions and we'll start with classics or popular ones:
Naruto (shonen, action, comedy)
xxxHolic (neither shonen or shojo, fantasy in a modern world, comedy, you may even say mystery)
Tsubasa Reservoir Chronicles (shonen, fantasy, romance, you may even say mystery)
Ouran High School Host Club (shojo, comedy, slice of life, and romance)
Chobits (can be shojo or shonen, science fiction, comedy, and romance)
Fruits Basket (shojo, slice of life, comedy, romance, and some magical things)
Elfen Lied (shonen, science fictoin, warning: There is gore and nudity)
Fairy Tail (shonen, action, adventure, fantasy, and comedy)
Those are many others but those are just some that got me interested in manga a lot.
Note: XxxHolic and Tsubasa Reservoir Chronicles overlap each other since they are made by the same group of artists, CLAMP (Chobits was too but it doesn't overlap). You can choose to read one or the other or both. But if you just choose to read one of them, it won't hinder you with any missing information or stuff like that.
Happy reading!