Starting to listen to Metal depends from person to person. Sometimes people are drawn by the rush of adrenaline and natural headbanging the fast, shocking and violent music gives them, so they start off with stuff that's a bit more heavy. Others escalate, from rock or punk to the glorious Metal and beyond. So I'll try to keep options available to your taste.
Try listening to The Best of Dio (Diamonds Album), along with Iron Maiden (The Number of the Beast, Piece of Mind, Brave New World, Killers, Maiden is freakin' great so you wont find alot
of not-so-epic albums there), Manowar, definitely (Warriors of The World United, Gods of War, Kings of Metal, Fighting the World). I would suggest Black Sabbath but they require a bit more Metal maturity first IMO, but the reference remains (Paranoid, Master of Reality). Judas Priest (the band that fucks up all sorts of genres and derivations. Simply pure, raw, awesome, Heavy Metal). Perhaps some Disturbed (I recall being really fund of them when I started listening to heavier music. Ten Thousand Fists, Indestructible). System of a Down (For some reason, most people I know including myself started listening to Metal with SOAD. Their music is sometimes so, different from everything else that even folks that aren't into Metal at all like them). Overall, if it is a band from the NWOBHM (New Wave Of British Heavy Metal) time period, like Saxon and others, you'll be good.
I would also recommend some Power Metal (something along the lines of Hammerfall, Blind Guardian, Gamma Ray, etc... Then venture off to YouTube and discover countless other bands in the "related" column. Seriously, it works).
If you feel ready for something more violent and aggressive, try the big names of thrash, and no, not just the "Big Four". Metallica (Ride The Lightning, the Black Album, Master of Puppets, Kill 'Em All), Megadeth (Countdown to Extinction, Rust In Peace, Youthanasia), Anthrax (Among The Living, Spreading The Disease, State of Euphoria), Slayer (God Hates Us All, Reign In Blood), Kreator (Pleasure To Kill, Coma of Souls), Exodus (Bonded By Blood, Shovel Headed Killing Machine), Sodom (M-16, Code Orange, In The Sign of Evil), Testament (Souls of Black, The Ritual, The Legacy), Destruction (Cracked Brain, Metal Discharge), among countless others you might discover (the world of Metal is experiencing a New Wave of Thrash Metal lately so there's alot
of stuff out there, but I would strongly suggest you listen to old-school stuff first).
From here, taste for other sorts of Metal is completely up to you to develop. If you go down the road of the Metalhead you'll end up enjoying nearly all styles of Metal, I speak for myself at least. Because that's a characteristic of Metal. It takes inspiration and musicality from other music genres, themes, topics and makes them better in an electrifying mix. Hell, 5 years from now I'd never thought I would one day enjoy stuff like Death and Black Metal, only to find out now they're the among the brütalest, Metalest things ever.
Hope this helped. Stay