I love anime, possibly a bit too much, so here's my advice:
Like PG said, manga would be a better place to start, but meh, it's your choice.
Personally, I prefer Sci-fi over fantasy, but you can't please everyone at once, so I'd reccomend making it the setting that you want to start with.
Remember it's a hobby, not a chore. If you start one anime/manga and you dont like it, stop! Start again or do a different story. But, don't completely give up if you
In my experience, good anime have a perfect balance of action, characters and good ol' "Uuuhh...what?" factor. Take Neon Genesis Evangelion for example. You got the bigz Robawt pwning noobs, then you have Shinji's troubles with the other pilots and his father, then you have wierd stuff happening.(Like the Eva activating itself, or the whole Rei character, for example).
Remember, whatever you do, keep making stuff happen! What put me off Naruto was that it seemed that whenever there was a fight, they just sorta stood there and gave eachother dirty looks and chatted for like, 2 episodes, and It just stood completely still for ages without anything significant happening! On the same note, make the setting interesting aswell! In Tengo Tenje; They went to a bowling alley, and even though there were cool fights and all, they were there for like, 5 or 6 episodes and it just got boring! I wanted to see somewhere else!
All in all, I would say keep it balanced between action and socials, make it unpredictable, so the people want to read the next episode, and finally, make it UNIQUE. Nobody want's another DBZ copy, nobody want's another Naruto copy.
And that's me done. Good luck, and I look forward to watching/reading it!