Le Chavvy Don has a decent first episode and then becomes boring as hell. I've failed to complete, or even get far into it, and I've had two attempts at doing so.
Handset hack your player and order the following:
Berserk
The Berserk manga is one of the most loved in existence. The Berserk anime covers the best part of the manga. You do the math.
It's dark, disturbing and has excellent characterization. It's the sort of thing adults can enjoy, though kids will also get a kick out of it because of all the blood.
Gungrave
Gungrave is perfect for anime fans who like The Godfather. It's about two street punks rising to the top of a crime syndicate, eventually turning against each other.
Its execution is very similar to Berserk - they start in the present of the stories and then jump into the past following the first episode.
Now and Then, Here and There
The best 13 episode series in existence. Not as well known as others because of how depressing it is, it being a tale of child slavery and war, but it blows near enough everything else away.
Wolf's Rain
While I rated the main series 8/10 and only the four episode OVA got a 9/10 from me, it's hard not to like Wolf's Rain. Great visuals, great music, wolves as main characters and none of the usual anime silliness.
There are other titles I could list, but if you go with these four you'll own four of the best series out there for under £18 each, and they'll last you for a lengthy period if you have a life.
Gankutsuou, an adaptation of The Count of Monte Cristo, is my favourite series. If you have good taste and aren't an idiot, check it out. Who can't appreciate an in-depth revenge story?
A R2 Death Note box set is coming out soon. Death Note is a story about someone getting a notebook that kills anyone whose name is wrote in it, meaning it's plenty dark enough for adults. It's also mysterious enough for you because as Light, the lead, tries to shape the world to his liking with the notebook, he's forced to enter into a battle of the minds against the greatest detective on the planet, L - they both attempt to discover the identity of the other from a distance.
And, finally, GTO. Read the manga instead of watching the anime. The anime skips and/or changes a lot of content, and the filler is awful. I rate the manga 9.5-10/10 and the anime 8/10. There's a difference.