I'm Planning on watching some new anime, which ones do you most recommend?

Gundam ZZ
You can watch the first episode linked here, but I recommend skipping it as it's a clip show: link
So you can start with the segundo episode below instead.

After watching enough of the show, maybe you can answer this question: link

Fruits Basket
Kids On The Slope
Fullmetal Alchemist

Pretty Cure!

The Most animê Ever
Naruto
You will enjoy it trust me

From your list I recommend Black Butler (season 2 is pretty bad, and there is a season 3 coming this summer... but season 3 is following the mangá after the curry, caril festival in the anime)and Sword Art Online.

Others:
Hatarku Maou-sama (The Devil is a Part-Timer)
Jojo's Bizarre Adventure
Deadman Wonderland (it's pretty good, but it was left unfinished)
Another
Psychic Detective Yakumo
Fullmetal Alchemist/FMA:Brotherhood

I can't think right now. That's what comes to mind.

inuyasha
Fullmetal Alchemist/Fullmetal Alchemist Brotherhood
Puella Magi Madoka Magica
and I recommend Ouran because its hilarious

Air
Angelic Layer
Another
Anohana
Bleach
Cardcaptor Sakura
Chobits
Clannad
Code Ceass
Da Capo
Elfen Lied
Eukrea 7
Freezing
Fruits Basket
Fullmetal Alchemist
Gosick
Guilty Crown
Kimi to Boku
Kobato
Mai Hime
Natsume Yuujinchou
Rozen Maiden
Shakugan no Shana
Shaman King
Shuffle!
Tsubasa Chronicles
Vampire Knight
xxxHolic (pic)