You're talking about an entire MEDIUM. Are the most popular films the best films?Texas America Murphy said:-Snip-
Cowboy Bebop is a pretty great show with a pretty great story (there are a few pretty terrible episodes though). But while a lot of it is episodic, the key story episodes really build on one another, so watching them out of order would be hard.
I don't watch Code Geass, so I have no idea there. It never looked particularly appealing to me, but that's all I can really say.
Though I was initially very reticent regarding Naruto, it really is popular for a reason. There are some nonsensical elements (the orange jumpsuit always seemed especially dumb), but it's a remarkably well-thought-out world and, despite what you saw, has some of the most pronounced character development in popular anime. Two things to remember though: (1) it's made primarily for kids and (2) it's HUNDREDS of episodes long, so the character development is appropriately slow and fairly subtle most of the time. It usually has wonderful animation and the thought that typically goes into how the abilities of the characters get used always impressed me, though your opinions might differ (a lot of the characters use their signature abilities in a large variety of ways, sometimes in very clever and complicated combinations, rather than just doing the same thing over and over like you see in some anime). The characters are incredibly obnoxious at first, but they're essentially supposed to be - they're immature little brats trying to figure out what they're supposed to be doing. Naruto is very much a coming-of-age story and most of the annoyingly childish character traits slowly vanish in a very believable way. You WILL hate the phrase "BELIEVE IT" if you ever watch the English dub though. Edit: Just saw post above mine, very well put.
Gurren Lagann is completely ridiculous, but that is ENTIRELY the point. Did you really think the giant robots with sunglasses were supposed to be taken seriously? It's probably a hard anime to like if you haven't ever watched anime though given that it's a parody of anime (with a hearty addition of many absurdist elements). It's also pretty emphatically not a kid's show, though it parodies those at several points too.
If you're interested in really trying anime, you might look into some of the more serious OVAs (the darker, edgier, shorter, higher-quality direct-to-video releases of the anime world) first given your interest in film. There're a decent number of OVAs outside of the fantasy/sci-fi/vaguely historical fiction genres that encompass the overwhelming majority of anime. As for some particularly good non-OVA series: FLCL (absurdist, amazing English dub, only about two hours long in total, and just really fucking weird (do not expect to understand what's going on at all the first time you watch it)), Serial Experiments: Lain (I watched this years ago and remember being blown away by the complexity and the philosophy, but I'm not sure how I'd feel about it if I watched it now), Cowboy Bebop (classic, discussed above), and Fullmetal Alchemist (fairly dark, relatively mature, great storyline, and a compelling setting and premise). Wolf's Rain is great too, though not the most straightforward if you're having trouble following what's going on in the anime you've watched so far. Ghost in the Shell is also GLORIOUS cyberpunk goodness with a serious focus on modern political issues. It's often confusing and the plots tend to be very intricate, but it's potentially a more familiar type of plot (technothriller in film terms), so if you're into that sort of thing, it might not be too hard.
Edit: Also, I didn't like Neon Genesis Evangelion. Most people disagree, but I think it was a messy attempt at more seriously giant robot anime that ended up confusing, illogical, and downright bad. You will find an awful lot of people (whether willing to admit it or not) that talk about how profound and thought-provoking the series is just to mask the fact that they didn't understand it (especially nearer the end). Having understood what was going on near the end, I didn't find it particularly appealing and it's CERTAINLY not a good introduction to anime.
Deathnote is like the new Evangelion. PROFOUNDLY overrated and even the people who like it will tend to agree that it should have ended much earlier than it did.