I've watched a ton of anime but only got into manga fairly recently so I'll focus on good beginner manga but I'll throw out a few anime first.

Since you liked Death Note I think you'd like One Outs which has the same level of mind games and strategy but is about a baseball pitcher with an unusual contract. Also from the same author of Death Note is Bakuman. which is about two teenagers who decide to make manga together. It plays out a bit like a sports show in that they have rivals and compete with them quite a bit. Also has some nice romance as well. You learn quite a bit about the manga industry as well.

Shirobako does the same thing that Bakuman. does for manga, but for anime.

As far as manga goes I mostly stick with completed series as I don't have the patience to wait month to month for translations. These are all complete series:

Goodnight PunPun This is a pretty heavy series but it's a masterpiece. Solanin by the same author is shorter and a bit more accessible though.

20th Century Boys, Planetes (also has a great anime), Saturn Apartments, Koe no Katachi, Memories of Emanon, Lucifer and the Biscuit hammer, Yokohama Kaidashi Kikou. I sort of ran out of steam with giving write ups, but those are all really great and worth looking into, and they are all complete and translated.