Probably not so good for a kind of gateway anime but No Game No Life will forever be a favourite of mine. It was the best anime by far last season.
Basically a pair of siblings who have never been beaten at any game get dropped into a world presided over by the God of Play, where everything is decided by games, including positions of power, national borders and so on. It's a really funny anime with loads of great moments and the artstyle cannot be described by words adequately, to say it's vibrant and colourful does not do it justice.
Every frame should inspire this
I'll add the old hats of Code Geass and Death Note for legit gateway anime since you're new, Code Geass is still up there in my top ten in fact, it's about a guy raising an army from nothing against an evil dictatorship with the power to make anyone obey his command through direct eye contact (actually a really limited power surprisingly) and a copious helping of mechas. They try a dual protagonist like Death Note did but honestly I grew to despise Suzaku after roundabout Episode 5/6, whenever he declines to join up with Zero and in my opinion, the second protagonist quickly becomes just another obstacle in the road for Lelouch and all sympathy towards him is lost. This may have been intentional but i'm unsure.
Another thing is the total ham in the voice acting in both the English and Japanese dubs is so much fun... JYB is so good at the whole anti-hero thing, he can carry the English dub on his own even if you disliked every other voice. Thankfully he doesn't need to cuz it's one of the better dubs out there but he really could.
"Now this new power, it's mine...
Well then."