You guys are nuts calling Ariel the worst.
Ariel's a strong and independent young girl (not quite a woman yet, if you ask me). In the first couple scenes of the movie, she's basically a young Lara Croft, digging up lost treasure and fucking around with the baddest mofos in the ocean (sharks) without an ounce of fear. She's got a major case of "the grass is always greener on the other side of the fence" because as a Princess she's given basically anything she wants, but she would rather risk her life for a piece of obscure treasure than live a shallow life singing songs about how great her daddy is. And while we're shown that a simple human fork is a goddamn treasure to her, she drops that shit in an instant, without an ounce of hesitation when her best friend (Flounder) is in trouble and she's needed to back him up.
She's got a massive hoard filled to overflowing with hard-earned contraband treasures, and even though each one is literally a treasure to her, she recognizes that they're hollow and that she wants something fundamentally deeper than her fangirl hobby.
Then she meets her Prince Charming and falls in love, and swims away from that back to the reality of her simple fangirl treasure cave.
Then her father storms in and violently smashes everything she cares about, so she runs away from home, selling her voice to a sketchy loan shark in exchange for a bus ticket. It's only after her father tried to destroy her entire identity (oh wow, she's a wealthy princess, she has everything, what's her problem, so spoiled [/sarcasm]) that she decided lay everything on the line to try and find Prince Charming and see if she can crash at his place.
Ursula stacked the deck against Ariel, unfairly turning it into a bet about whether or not Ariel can get Prince Charming to kiss her, and Ariel easily beat those unfair odds (because she's a mega hottie, beautiful voice or no voice). So Ursula had to intervene and cheat directly. And Ariel still almost won (came within about a second of winning), despite Ursula cheating as hard as possible (up to and including mind control over Prince Charming).
Ariel didn't doom the undersea kingdom, she walked away from it. Ariel's dad doomed the undersea kingdom, deliberately, because he felt he needed to step in and save Ariel from the situation he pushed her into. And then Ariel and Prince Charming solved the "doom" problem by murdering Ursula, liberating Ariel's dad. And they all lived happily ever after. The End.