I think, based on some of the earlier posts you made about unresolved tension and lack of understanding after the first episode, that you may be missing a piece of fundamental information regarding anime.
It's all part of one story, they are not 'episodes' as such, much segments of a long film, do not expect to fully understand them after the first few pages, so to speak.
If you already understood that, then sorry, my bad =)
Secondly, Cowboy Bebop should be good, enjoy, and if that doesn't hook you try this [http://www.animefreak.tv/watch/claymore-episode-1-english-dubbed-online-free#English]. I was pretty much in the same boat as you a short while ago, maybe a few months, I pretty much thought that all anime was a massive waste of time, full of stereotypical characters with oversized breasts. I watch one episode of Claymore on a friends request, and got hooked.
My advice is, don't look at these things with the eyes of a critic, just try to enjoy it. When I pick apart the music I like in my head (as a musician) I find things I would've liked done another way, and it can destroy what I would otherwise have got out of it. On top of this, there is a massive psychological correlation between what you expect to feel/see/e.t.c, and what you do - so much so, that it is actually possible to fool people into believing they are eating different flavoured sweets depending purely on what colour they are.
Remember this, and approach anime with a genuinely open mind, not thinking about what snarky remarks you will post on the forums later.
I really hope you end up liking anime, because, to be honest, if you can just suspend your disbelief sufficiently, and become immersed in it (as you would a video game or book), it can be a great way to unwind, and to fuel your imagination. Good luck =)
Also, I would advise that you watch subbed, as bad voice acting (acting in general) can ruin any media.