First of if your brand new don't pick a series like Bleach, Naruto, Sailormoon, Dragon Ball (Z), One Piece heck any series with episodes numbering in the 100's. Start with a movie, Akira or any of the Studio Gibili(sp) are prefrebable (note Akira is very much a condensed version of 1000+ page comic made for its fans who already knew the plot, but it is a traditional gateway), these will introduce the artstyle and conventions better than jumping into the middle of a long running story. Then you really need to think what it is that intreasts you. Look for a mini-series of about 12/13 episodes in your chosen Genre. If I was going to recommend at this point I would say look for FLCL (very pathonesque with its nonesequiters) or Parionia Agent which is series of stories about people with messed up lives and how there lives are turned around by a brutal assualt. Then look for a 26 or 52 episode series such as:
Evangelion, RahXaphon (both these series have very confusing endings and require mutiple viewings)
Excel Saga (very much a nonsequiter gag show)
AzuManga Daioh (very much a sketch show)
One of the solo Gundams such as Wing and Seed (avoid seed destiny, the main charecters from seed are replaced and its just not as good)
The Vision of Escaflowne (Gundam but in a fantasy setting and most excellent)
Full Metal Alchemist (not seen but I hear its higly recommended)
(Note: Avoid any movies based on a longer series as they are genrally either retellings and thus full of spoilers or epilogues/subtales and thus difficult to understand.)
Now your ready for one of the longer shows, Bleach is good but avoid the filler arcs with avengence. Others to consider are Ranma 1/2, Naruto, Pokemon (if you can stand it), One Piece, Sailormoon, theres litteraly hundreds of these long running shows and you'll find supporters and detractors for each one. Though a universal truth for all of them is that filler arcs are chud.
Hope this helps.
((Edit: Avoid Urosukidoji and La Blue Girl unless you want to fap and/or be mentally scarred for life))