Start with something simple like one punch man. A lot of people try to get into the 100+ episode classics off the bat and then thing they don't like anime. But you have to develop a pallet for it
That's what I've found: there's a dozen or so series that are great going back decades that I've found. But whenever an anime fan or friend recommends some, 80% of the time there's fanservice that is so out of place. I ended up just ignoring most anime for that reason.
You can have sex and nudity, even gratuitous (like many HBO shows), but the casual objectification without even recognizing it puts me off.
I feel different from most anime fans in that sometimes I can ignore it and other times it's worth dropping the series. A little fan service and cringe nosebleed scenes are just standard anime tropes at this point. But some anime pushes it so far that, like you said, its jarring and distracts from the story. I've dropped a few shows just for the annoying fan service alone (Fireforce, Fairytale, Seven deadly sins, etc.)
If you are looking for recommendations of shonen anime that have heart, action, and deep characters I would suggest: Mob Psycho 100 and Ping Pong the Animation. Both of these have a weird art style, but they both have a story to tell that leaves a deep impact on you.
That said, anime is a a big medium and there is something that will appeal to everyone (dramas, sci-fi, romance, ecchi, sports, mecha, horror, comedy, historical fiction, etc.) I've linked some helpful anime flowcharts/recommendations that I always refer to when I want to get away from the endless deluge of seasonal anime.
I wish that first one with content warnings and flowcharts defined what they considered NSFW and Bloody content. Just glancing first off, I watched One Punch Man but don't recall NSFW content. Maybe that girl in the green dress?
Inuyasha, Dragonball, Ranma ½, Fist of the North Star, Lupin the third, Urusei Yatsura, Jojo, Legend of the Galactic Heroes, Hunter x Hunter and a bunch of others.
Some are good, some are definitely classic, and a few are both.
Mostly because it's not sourced from, or meant to be, weekly episodic content. It's from a set of space opera novels, so the animated version is like when people adapt Game of Thrones. It's also technically not an Anime, but an OVA.
There's nothing really cringe about it. Just good story in an animated format.