I started with Azumanga Daioh (slice of life anime about school life), One Piece (sea adventure anime about rubber boy) and K-ON! (school band of cute girls).

Honestly don't worry about being perceived as cringe for liking a particular anime (with exemptions of course; stay away from the shit with children), whatever vibes with you.

I recommend reading the manga first before watching the anime; a lot more background and characterization often occurs there.