It's depends on the kind of stuff you like as anime itself isn't a genre; it has action, fantasy, horror etc.
the first anime i saw was detective conan but i didn't follow it I just watched it now and again.
the first anime i finished was probably naruto (a boy who is an outcast tries to become the ultimate ninja) but the following are all good animes as well:
bleach - talks about death-gods, has a lot of fighting, some comedy
one piece - a boy who wants the ultimate pirate treasure, some people have weird powers because of eating the devil fruit
full metal alchemist/FMA: brotherhood - a world where alchemy is studied as a science, 2 boys fight to regain their original bodies (slightly complex to explain)
death note - a super intelligent boy finds a notebook, if you write anyones name in the notebook they die
avatar: the last airbender is ok as well - a boy who can control all four elements trying to stop tyranny and war (it's not Japanese though, english)
these are just some animes there are loads more just explore different things and see what you like