So, yeah,
Any manga with Mc like in Gakuen Babysitters

Hmmmm, how is he,
1. Kinda innocent (I guess)
2. Extremely caring (this could be applied for both girls or kids, thanks)
3. Girls kinda admire him (for being adorable)
4. Not sure how to say it, but, he kinda have a 'good kid' aura or somethin...
(Ah, and the recs don't need to have all of these, but at least two, with the extremely caring characteristic in, please, thanks..)

Shoujos are fine too, but I prefer male being the Mc,

Thanks.. ^^

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Tournament Round 1
Round 2

the MC natsume in Natsume Yuujinchou is definitely like that

although i think natsume fits the best these also have similar main characters ones too, although they are more on the action side

07 Ghost
D. Gray Man
Tower of God

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Like educational manga? take a look at Ed U. Manga's list of manga here

Ore Monogatari!! Fits well for 1 and 2... but he doesn't seem to have much success with women (until the story starts that is)

Angel Densetsu Definitely good for all points (although not immediately for 3)

Gin no Saji Not sure about 1. But 2 and 4 should fit.

The Friendly Winter Maybe not what you're looking for because the MCs aren't exactly "normal" but it does fit 1, 2 and 4.

Shibutani-kun Tomo no Kai maybe?