Firstly watch some good anime. Heres a good list my current small list I recommend to newbies Air Gear Bishoujo Senshi Sailor Moon - Don't laugh because of the american version this anime lost rep. Find the japanese version and watch the lesbo sailor scouts kick more ass Black Blood Brothers Cowboy Bebop Darker than Black DearS Death Note Dragonaut: The Resonance Full Metal Panic! Ghost Hunt Girls Bravo - First Season Heroic Age Koukyoushi Hen: Eureka Seven Macross F RahXephon Rosario to Vampire Shinseiki Evangelion Soukyuu no Fafner: Dead Aggressor Suzuka Tengen Toppa Gurren Lagann Tokimeki Memorial: Only Love Tokyo Majin Gakuen Kenpuchou Tou Trigun Utawarerumono VanDread Zegapain Zombie-Loan My top 5 are inside that list. Anyway thats just a small list (about 10% of what I have watched) it should be a good list to get you started on your journey down the anime road. After you watch those if you need more I'll give you more but it would be best that you try and find what you like. This list has a little of everything.
The Animes I watched and which I can suggest are 1) Death Note 2) Trinity Blood or 3) Elfenlied I appreciated watching them.
Depends on what you're looking for One Piece if you like comedy + action. It has to be with English subs though cauz the English dubs are way to childish. Death Note or Code Geass if you like cool animes with action but strategy
Heres some of the best anime ive seen in a while other than Naruto and Bleach Death Note-This anime is about a guy that can instantly kill people by writing their names in a notebook, which was given to him by a death god, but there are certain laws he must follow and there are others out to track him down and catch him. Basically a battle of wits. Air Gear-An anime about skate crews(trust me, way cooler than it sounds) that battle to win the title of skyking and along they way they get special powered skates that kick@ss. One of my favorite animes. Both animes are only around 30 episodes I believe so they can be finished in no time at all.
Bleach and Nurato... you like action from what I can tell. You should watch (sorry if i repeat any mentioned before, i haven't read anything) Shakugan no Shana, Fate/Stay Night, Claymore, Rurouni Kenshin, and Samurai Champloo. I like action and I've liked these so far. Although becareful with Samurai Champloo, its kinda mature.