Steins;Gate

Doesn't has the best animation, nor exaggerated action scenes, but if you want to suggest an anime to someone this is the safest bet. The story unravels itself slowly from a struggling scientist to saving the world, there are many times where it presents stark contrast between delusions and reality, and even combining them, and then shattering them to dust. The story keeps getting better every episode you progress through and also has many comedic elements to keep you attached.