If you want something simple to learn the rules on, fighter, rogue, or barbarian would be my go-to. Anything spellcaster-related is going to have a lot of homework to learn all the spells and the most strategically efficient ways to use them.
@FaeLuna the mage used to be my favorite for the original game. I guess if that world actually existed I'd be a mix between a mage and fighter. A hybrid.
@Encontrados I mean, multiclassing [i]is[/i] a thing you can do. I wouldn't recommend it for a first time player, though, because that gets even more complicated than one class.
Depends on what you want to do. Want to be in the thick of the fight? Be a fighter or barbarian. Want to be more subtle in your actions? Be a rogue or monk. Like supporting others and keeping everyone alive, while occasionally getting a few licks in? Be a cleric, paladin or a bard. Want to stalk the woods and fight from a distance? Be a ranger or druid. Interested in casting spells? Be a wizard, sorcerer or warlock. More interested in the social aspects of the game — schmoozing with folks, gathering information and so on? Bard or rogue.
Fifth edition has a lot of options, though. Eldritch knights are fighters who can cast a few wizard spells, for example. Bards are good if you're interested in a swashbuckling sort of character, swinging from chandeliers waving a rapier and casting spells.
I would suggest don't worry about the rules too much at this point, though. Create a character concept that appeals to you and get with your dungeon master to craft the class and race options to get a character reasonably close to your idea.
For new players I typically recommend something like a fighter or barbarian. Something whose job it is to smash everything.
Reason for that is sometimes it can be hard to figure out what you should do in any given situation. If your job is to punch things, well then you'll know to punch - as opposed to a wizard where you need to pick the right spells, or a rogue where you need to be clever.
But I mean... whatever excites you the most should be your first choice.
@WanderLustChick I recommend cleric. They give you a strong idea of what your character is, and always have something fun to do. I like bards a lot but their purpose can be a little opaque for a new player.
@WanderLustChick well dungeons usually have guards and they have to clock off. You can prize secrets out of them by ploughing them with alcohol then you become the go to lady, selling on your information and paid protection :-)