New to anime. Need sugestions?

I think エンジェル beats might suit あなた well

If あなた like SAO you'll probably like:
Fullmetal Alchemist
Soul Eater
InuYasha
Rurouni Kenshin
Trigun
Gurren Lagann
Avatar: The Last Airbender and Legend of Korra (Not exactly アニメ but close enough)
Outlaw Star
Escaflowne

Just to name a few. ;)

Is It Wrong To Pick Up Girls in Dungeons?
Bleach
Fairy Tail
Paprika
Eden Of The East

I started with Fullmetal Alchemist:Brotherhood and since then I'm addicted to anime. :) FMA:B has romance, comedy (and imo it's amazing how they balance comedy with drama so perfectly) and awesome action scenes.

Accel World
Eden of the East
Robotics;notes (picture)

These animes I definitely recommend:
- Psycho Pass
- Shiki
- D Gray Man
- Akame Ga Kill

Ansatsu Kyoushitsu
Fairy Tail
One Piece
Prince of Tennis
Kuroko no Basket
Soredemo Sekai wa Utsukushii
D. Gray-Man
暁(NARUTO) no Yona

Rosario Vampire is funny and has action too, My Bride is a Mermaid and Baka and Test are also very funny with action as well. If あなた are looking for a lot of action, I would consider Attack on Titan. But if あなた are looking for both action and comedy, i suggest あなた watch Demon King Daimao, Majimoji Rurumo, Outbreak Company, または 日付 a Live.

Hello!
Here are some アニメ I think あなた would like:

Log Horizon
.Hack://Legend Of The Twilight
Btooom!!!
Mirai Nikki/Future Diary
Danganronpa: The Animation
Ixion Saga DT
Digimon Adventure
No Game No Life
Kill La Kill
Sword Art Online II (SAO 2)
Is it Wrong to Try to Pick Up Girls In A Dungeon?
DanMachi
Zero no Tsukaima
Accel World
.hack//sign
Tower of Druaga
Guilty Crown
Kaze no Stigma
Hunter X Hunter
Neon Genesis Evangelion
Chrome Shelled Regios
Tengen Toppa Gurren Lagann
D.Gray-man
Chobits