Here's an idea: why not watch anime films instead?
The animation tends to be better, the story more solid, no option of having three episodes with nothing but boring stuff, etc. I'm thinking about half of the Ghibli library, Steamboy, Ghost In The Shell 1 & 2 (some forced "philosophic" overtones, but still nice), Manie Manie (called Neo Tokyo in the USA, I believe), Memories, Fallen Leaves (which isn't as "good" as it is just interesting), most of the stuff by Satoshi Kon, the Appleseed movies (good action, passable story) and Osamu Tezuka's Metropolis - which has one of the best climaxes ever (don't let the silly drawing style fool you).
Now, if you really HAVE to stick to series...
I'd recommend FLCL and Paranoia Agent. FLCL has quite a few of those annoying typical Japanese anime tropes (saying someone's name and then pausing, like they were about to say something, but they don't, it's just STUPID, WHAT ARE YOU TRYING TO SAY GODDA-) However, it is so energetic, so varied and so short (6 episodes) that I couldn't help having fun while watching it. I don't know if the english dub is any good though, since the Belgian version only had the French dub (which I didn't listen to, because French dubs always suck, anime or no). As for Paranoia Agent, it is also mercifully short (13 episodes?) and juggles around a lot of interesting concepts. I guess the finale might not please everyone, but it's a fun and interesting ride nonetheless.
The animation tends to be better, the story more solid, no option of having three episodes with nothing but boring stuff, etc. I'm thinking about half of the Ghibli library, Steamboy, Ghost In The Shell 1 & 2 (some forced "philosophic" overtones, but still nice), Manie Manie (called Neo Tokyo in the USA, I believe), Memories, Fallen Leaves (which isn't as "good" as it is just interesting), most of the stuff by Satoshi Kon, the Appleseed movies (good action, passable story) and Osamu Tezuka's Metropolis - which has one of the best climaxes ever (don't let the silly drawing style fool you).
Now, if you really HAVE to stick to series...
I'd recommend FLCL and Paranoia Agent. FLCL has quite a few of those annoying typical Japanese anime tropes (saying someone's name and then pausing, like they were about to say something, but they don't, it's just STUPID, WHAT ARE YOU TRYING TO SAY GODDA-) However, it is so energetic, so varied and so short (6 episodes) that I couldn't help having fun while watching it. I don't know if the english dub is any good though, since the Belgian version only had the French dub (which I didn't listen to, because French dubs always suck, anime or no). As for Paranoia Agent, it is also mercifully short (13 episodes?) and juggles around a lot of interesting concepts. I guess the finale might not please everyone, but it's a fun and interesting ride nonetheless.