What Anime Would Be Good For Me To Watch?

I don't know about anime but I HIGHLY suggest reading Solanin or What a Wonderful World. It's deep about the meaning behind life and finding happiness. It's psychological and has realistic art. It's by a guy named Asano Inio. Solanin is probably my favorite manga and it made me cry for reasons I cna't even explain.

It's also super funny!

Both Fullmetal Alchemist versions are good. They each raise different thought-provoking questions (they're very different from each other, actually, despite having the same name).

Also, Steins;Gate totally blew my mind away, because it actually takes time travel seriously and doesn't give a random deus ex machina ending.

I would also recommend Ano Hi Mita Hana no Namae o Bokutachi wa Mada Shiranai, which is a bildungsroman (story about growth and maturation of character(s)) with a good bit of depth, accompanied by enough comedy to keep it appropriately light hearted.

Lucky Star also blew my mind away, but in a totally different way; the more familiar you are with the anime world, the funnier you'll find it, because it's choke full of references and parodies (instead of just randomly tossing them into a piece of work, it's masterfully woven together). For the same reason, I would also recommend Hayate no Gotoku.

Serial Experiment Lain

Bleach is really good. If you're looking for depth and great characters, then this anime is for you.

I would try Durarara!!